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The effects of lockdown during the COVID-19 pandemic on fetal movement profiles (2024)
Journal Article
Reissland, N., Ustun, B., & Einbeck, J. (2024). The effects of lockdown during the COVID-19 pandemic on fetal movement profiles. BMC Pregnancy and Childbirth, 24(1), 56. https://doi.org/10.1186/s12884-024-06259-8

Purpose: The current study investigated the direct impact of the COVID-19 lockdown on fetal movements, addressing a critical research gap. While previous research has predominantly examined the effects of lockdown on maternal health and postnatal out... Read More about The effects of lockdown during the COVID-19 pandemic on fetal movement profiles.

A Versatile Model for Clustered and Highly Correlated Multivariate Data (2024)
Journal Article
Zhang, Y., & Einbeck, J. (2024). A Versatile Model for Clustered and Highly Correlated Multivariate Data. Journal of statistical theory and practice, 18(1), Article 5. https://doi.org/10.1007/s42519-023-00357-0

For the analysis of multivariate data with an approximately one-dimensional latent structure, it is suggested to model this latent variable by a random effect, allowing for the use of mixed model methodology for dimension reduction purposes. We imple... Read More about A Versatile Model for Clustered and Highly Correlated Multivariate Data.

A fresh look at mean-shift based modal clustering (2023)
Journal Article
Ameijeiras-Alonso, J., & Einbeck, J. (2023). A fresh look at mean-shift based modal clustering. Advances in Data Analysis and Classification, https://doi.org/10.1007/s11634-023-00575-1

Modal clustering is an unsupervised learning technique where cluster centers are identified as the local maxima of nonparametric probability density estimates. A natural algorithmic engine for the computation of these maxima is the mean shift procedu... Read More about A fresh look at mean-shift based modal clustering.

A Sequential Cross-Sectional Analysis Producing Robust Weekly COVID-19 Rates for South East Asian Countries (2023)
Journal Article
Almohaimeed, A., & Einbeck, J. (2023). A Sequential Cross-Sectional Analysis Producing Robust Weekly COVID-19 Rates for South East Asian Countries. Viruses, 15(7), Article 1572. https://doi.org/10.3390/v15071572

The COVID-19 pandemic has expanded fast over the world, affecting millions of people and generating serious health, social, and economic consequences. All South East Asian countries have experienced the pandemic, with various degrees of intensity and... Read More about A Sequential Cross-Sectional Analysis Producing Robust Weekly COVID-19 Rates for South East Asian Countries.

Use of a targeted, computer/web-based guided self-help psychoeducation toolkit for distressing hallucinations (MUSE) in people with an at-risk mental state for psychosis: protocol for a randomised controlled feasibility trial (2023)
Journal Article
Hamilton, J., Arnott, B., Aynsworth, C., Barclay, N. A., Birkett, L., Brandon, T., …Fernyhough, C. (2023). Use of a targeted, computer/web-based guided self-help psychoeducation toolkit for distressing hallucinations (MUSE) in people with an at-risk mental state for psychosis: protocol for a randomised controlled feasibility trial. BMJ Open, 13(6), Article e076101. https://doi.org/10.1136/bmjopen-2023-076101

Individuals who access at-risk mental state (ARMS) services often have unusual sensory experiences and levels of distress that lead them to seek help. The Managing Unusual Sensory Experiences (MUSE) treatment is a brief symptom targeted intervention... Read More about Use of a targeted, computer/web-based guided self-help psychoeducation toolkit for distressing hallucinations (MUSE) in people with an at-risk mental state for psychosis: protocol for a randomised controlled feasibility trial.

Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions (2023)
Journal Article
Bar-Lev, S. K., Batsidis, A., Einbeck, J., Liu, X., & Ren, P. (2023). Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions. Mathematics, 11(7), Article 1603. https://doi.org/10.3390/math11071603

The class of natural exponential families (NEFs) of distributions having power variance functions (NEF-PVFs) is huge (uncountable), with enormous applications in various fields. Based on a characterization property that holds for the cumulants of the... Read More about Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions.

Association between Hyperemesis Gravidarum in pregnancy on postnatal ability of infants to attend to a play task with their mother (2023)
Journal Article
Reissland, N., Matthewson, J., & Einbeck, J. (2023). Association between Hyperemesis Gravidarum in pregnancy on postnatal ability of infants to attend to a play task with their mother. Infant Behavior & Development, 71, https://doi.org/10.1016/j.infbeh.2023.101823

Research indicates a higher prevalence of attention deficits in children exposed to HG in utero compared to controls with some claiming that the deficit is due to prenatal effects of malnutrition in HG mothers and others that it is due to maternal me... Read More about Association between Hyperemesis Gravidarum in pregnancy on postnatal ability of infants to attend to a play task with their mother.

Biodose Tools: an R shiny application for biological dosimetry (2023)
Journal Article
Hernández, A., Endesfelder, D., Einbeck, J., Puig, P., Benadjaoud, M. A., Higueras, M., …Barquinero, J. F. (2023). Biodose Tools: an R shiny application for biological dosimetry. International Journal of Radiation Biology, 99(9), https://doi.org/10.1080/09553002.2023.2176564

Introduction: In the event of a radiological accident or incident, the aim of biological dosimetry is to convert the yield of a specific biomarker of exposure to ionizing radiation into an absorbed dose. Since the 1980s, various tools have been used... Read More about Biodose Tools: an R shiny application for biological dosimetry.

Using Random Effect Models to Produce Robust Estimates of Death Rates in COVID-19 Data (2022)
Journal Article
Almohaimeed, A., Einbeck, J., Qarmalah, N., & Alkhidhr, H. (2022). Using Random Effect Models to Produce Robust Estimates of Death Rates in COVID-19 Data. International Journal of Environmental Research and Public Health, 19(22), https://doi.org/10.3390/ijerph192214960

Tracking the progress of an infectious disease is critical during a pandemic. However, the incubation period, diagnosis, and treatment most often cause uncertainties in the reporting of both cases and deaths, leading in turn to unreliable death rates... Read More about Using Random Effect Models to Produce Robust Estimates of Death Rates in COVID-19 Data.

A robust Bayesian analysis of variable selection under prior ignorance (2022)
Journal Article
Basu, T., Troffaes, M. C., & Einbeck, J. (2023). A robust Bayesian analysis of variable selection under prior ignorance. Sankhya A - Mathematical Statistics and Probability, 85(1), 1014-1057. https://doi.org/10.1007/s13171-022-00287-2

We propose a cautious Bayesian variable selection routine by investigating the sensitivity of a hierarchical model, where the regression coefficients are specified by spike and slab priors. We exploit the use of latent variables to understand the imp... Read More about A robust Bayesian analysis of variable selection under prior ignorance.

The impact of a novel medication scanner on administration errors in the hospital setting: a before and after feasibility study (2022)
Journal Article
Tolley, C. L., Watson, N. W., Heed, A., Einbeck, J., Medows, S., Wood, L., …Slight, S. P. (2022). The impact of a novel medication scanner on administration errors in the hospital setting: a before and after feasibility study. BMC Medical Informatics and Decision Making, 22(1), Article 86. https://doi.org/10.1186/s12911-022-01828-3

Objective: The medication administration process is complex and consequently prone to errors. Closed Loop Medication Administration solutions aim to improve patient safety. We assessed the impact of a novel medication scanning device (MedEye) on the... Read More about The impact of a novel medication scanner on administration errors in the hospital setting: a before and after feasibility study.

Effects of maternal mental health on prenatal movement profiles in twins and singletons (2021)
Journal Article
Reissland, N., Einbeck, J., Wood, R., & Lane, A. (2021). Effects of maternal mental health on prenatal movement profiles in twins and singletons. Acta Paediatrica: Nurturing the Child, 110(9), 2553-2558. https://doi.org/10.1111/apa.15903

Aim: Prenatal experiences, including maternal stress, depression and anxiety, form crucial building blocks affecting the maturation of the fetal central nervous system. Previous research has examined fetal movements without considering effects of mat... Read More about Effects of maternal mental health on prenatal movement profiles in twins and singletons.

The effect of data aggregation on dispersion estimates in count data models (2021)
Journal Article
Errington, A., Einbeck, J., Cumming, J., Rössler, U., & Endesfelder, D. (2022). The effect of data aggregation on dispersion estimates in count data models. International Journal of Biostatistics, 18(1), 183-202. https://doi.org/10.1515/ijb-2020-0079

For the modelling of count data, aggregation of the raw data over certain subgroups or predictor configurations is common practice. This is, for instance, the case for count data biomarkers of radiation exposure. Under the Poisson law, count data can... Read More about The effect of data aggregation on dispersion estimates in count data models.

Multisite educational trials: estimating the effect size and its confidence intervals (2021)
Journal Article
Singh, A., Uwimpuhwe, G., Li, M., Einbeck, J., Higgins, S., & Kasim, A. (2022). Multisite educational trials: estimating the effect size and its confidence intervals. International Journal of Research & Method in Education, 45(1), 18-38. https://doi.org/10.1080/1743727x.2021.1882416

In education, multisite trials involve randomisation of pupils into intervention and comparison groups within schools. Most analytical models in multisite educational trials ignore that the impact of an intervention may be school dependent. This stud... Read More about Multisite educational trials: estimating the effect size and its confidence intervals.

Response transformations for random effect and variance component models (2020)
Journal Article
Almohaimeed, A., & Einbeck, J. (2022). Response transformations for random effect and variance component models. Statistical Modelling, 22(4), 297-326. https://doi.org/10.1177/1471082x20966919

Random effect models have been popularly used as a mainstream statistical technique over several decades; and the same can be said for response transformation models such as the Box–Cox transformation. The latter aims at ensuring that the assumptions... Read More about Response transformations for random effect and variance component models.

A graphical tool for assessing the suitability of a count regression model (2020)
Journal Article
Wilson, P., & Einbeck, J. (2021). A graphical tool for assessing the suitability of a count regression model. Austrian Journal of Statistics, 50(1), 1-23. https://doi.org/10.17713/ajs.v50i1.921

Whilst many numeric methods, such as AIC and deviance, exist for assessing or comparing model fit, diagrammatic methods are few. We present here a diagnostic plot, which we refer to as a `Quantile Band plot', that may be used to visually assess the s... Read More about A graphical tool for assessing the suitability of a count regression model.

Improving the accuracy of dose estimates from automatically scored dicentric chromosomes by accounting for chromosome number (2020)
Journal Article
Endesfelder, D., Kulka, U., Einbeck, J., & Oestreicher, U. (2020). Improving the accuracy of dose estimates from automatically scored dicentric chromosomes by accounting for chromosome number. International Journal of Radiation Biology, 96(12), 1571-1584. https://doi.org/10.1080/09553002.2020.1829152

Purpose: The traditional workflow for biological dosimetry based on manual scoring of dicentric chromosomes is very time consuming. Especially for large-scale scenarios or for low-dose exposures, high cell numbers have to be analysed, requiring alter... Read More about Improving the accuracy of dose estimates from automatically scored dicentric chromosomes by accounting for chromosome number.

Effects of maternal mental health on fetal visual preference for face-like compared to non-face like light stimulation (2020)
Journal Article
Reissland, N., Wood, R., Einbeck, J., & Lane, A. (2020). Effects of maternal mental health on fetal visual preference for face-like compared to non-face like light stimulation. Early Human Development, 151, Article 105227. https://doi.org/10.1016/j.earlhumdev.2020.105227

The question of whether humans react differentially to face-like versus non face-like light stimulation in the prenatal period has been much discussed, but to date has remained unresolved. In this feasibility study we have come closer to understandin... Read More about Effects of maternal mental health on fetal visual preference for face-like compared to non-face like light stimulation.

Prenatal effects of maternal nutritional stress and mental health on the fetal movement profile (2020)
Journal Article
Reissland, N., Millard, A., Wood, R., Ustun, B., McFaul, C., Froggatt, S., & Einbeck, J. (2020). Prenatal effects of maternal nutritional stress and mental health on the fetal movement profile. Archives of Gynecology and Obstetrics, 302(1), 65-75. https://doi.org/10.1007/s00404-020-05571-w

Purpose: Prenatal sub-optimal nutrition and exposure to maternal stress, anxiety and depression in pregnancy have been linked to increased postnatal morbidity and mortality. Fetal growth is most vulnerable to maternal dietary deficiencies, such as th... Read More about Prenatal effects of maternal nutritional stress and mental health on the fetal movement profile.

Testing fetal abilities: A commentary on studies testing prenatal reactions to light stimulation (2020)
Journal Article
Reissland, N., Wood, R., Einbeck, J., & Lane, A. Testing fetal abilities: A commentary on studies testing prenatal reactions to light stimulation. Manuscript submitted for publication

In utero conditions on fetal neurodevelopment are of current concern. One aspect relates to the question of the effects of maternal mental health and maturity of the fetus on prenatal neurodevelopment. In this feasibility study, we examined the as ye... Read More about Testing fetal abilities: A commentary on studies testing prenatal reactions to light stimulation.

Practical Considerations on Nonparametric Methods for Estimating Intrinsic Dimensions of Nonlinear Data Structures (2019)
Journal Article
Einbeck, J., Kalantan, Z., & Kruger, U. (2020). Practical Considerations on Nonparametric Methods for Estimating Intrinsic Dimensions of Nonlinear Data Structures. International Journal of Pattern Recognition and Artificial Intelligence, 34(9), Article 2058010. https://doi.org/10.1142/s0218001420580100

This paper develops readily applicable methods for estimating the intrinsic dimension of multivariate datasets. The proposed methods, which make use of theoretical properties of the empirical distribution functions of (pairwise or pointwise) distance... Read More about Practical Considerations on Nonparametric Methods for Estimating Intrinsic Dimensions of Nonlinear Data Structures.

Quantile-Based Estimation of the Finite Cauchy Mixture Model (2019)
Journal Article
Kalantan, Z. I., & Einbeck, J. (2019). Quantile-Based Estimation of the Finite Cauchy Mixture Model. Symmetry, 11(9), Article 1186. https://doi.org/10.3390/sym11091186

Heterogeneity and outliers are two aspects which add considerable complexity to the analysis of data. The Cauchy mixture model is an attractive device to deal with both issues simultaneously. This paper develops an Expectation-Maximization-type algor... Read More about Quantile-Based Estimation of the Finite Cauchy Mixture Model.

A statistical framework for radiation dose estimation with uncertainty quantification from the γ-H2AX assay (2018)
Journal Article
Einbeck, J., Ainsbury, E. A., Sales, R., Barnard, S., Kaestle, F., & Higueras, M. (2018). A statistical framework for radiation dose estimation with uncertainty quantification from the γ-H2AX assay. PLoS ONE, 13(11), https://doi.org/10.1371/journal.pone.0207464

Over the last decade, the γ–H2AX focus assay, which exploits the phosphorylation of the H2AX histone following DNA double–strand–breaks, has made considerable progress towards acceptance as a reliable biomarker for exposure to ionizing radiation. Whi... Read More about A statistical framework for radiation dose estimation with uncertainty quantification from the γ-H2AX assay.

A new and intuitive test for zero modification (2018)
Journal Article
Wilson, P., & Einbeck, J. (2019). A new and intuitive test for zero modification. Statistical Modelling, 19(4), 341--361. https://doi.org/10.1177/1471082x18762277

While there do exist several statistical tests for detecting zero modification in count data regression models, these rely on asymptotical results and do not transparently distinguish between zero inflation and zero deflation. In this manuscript, a n... Read More about A new and intuitive test for zero modification.

Fisher information under Gaussian quadrature models (2017)
Journal Article
Marques da Silva Júnior, A. H., Einbeck, J., & Craig, P. S. (2018). Fisher information under Gaussian quadrature models. Statistica Neerlandica, 72(2), 74-89. https://doi.org/10.1111/stan.12116

This paper develops formulae to compute the Fisher information matrix for the regression parameters of generalized linear models with Gaussian random effects. The Fisher information matrix relies on the estimation of the response variance under the m... Read More about Fisher information under Gaussian quadrature models.

Self–consistency–based tests for bivariate distributions (2017)
Journal Article
Einbeck, J., & Meintanis, S. (2017). Self–consistency–based tests for bivariate distributions. Journal of statistical theory and practice, 11(3), 478-492. https://doi.org/10.1080/15598608.2017.1318098

A novel family of tests based on the self–consistency property is developed. Our developments can be motivated by the well known fact that a two–dimensional spherically symmetric distribution X is self–consistent w.r.t. to the circle E||X||, that is... Read More about Self–consistency–based tests for bivariate distributions.

Mixture Models for Prediction from Time Series, with Application to Energy Use Data (2017)
Journal Article
Qarmalah, N. M., Einbeck, J., & Coolen, F. P. (2017). Mixture Models for Prediction from Time Series, with Application to Energy Use Data. Archives of data science. Series A, 2(1), 1-15. https://doi.org/10.5445/ksp/1000058749/07

This paper aims to use mixture models to produce predictions from time series data. Given data of the form (ti, yi), i = 1, . . . , T , we propose a mix- ture model localized at time point tT with the k-th component as yi = mk (ti) + εik with mixing... Read More about Mixture Models for Prediction from Time Series, with Application to Energy Use Data.

The correlation threshold as a strategy for gene filtering, with application to irritable bowel syndrome and breast cancer microarray data (2016)
Journal Article
Jackson, S. E., Einbeck, J., Kasim, A., & Talloen, W. (2016). The correlation threshold as a strategy for gene filtering, with application to irritable bowel syndrome and breast cancer microarray data. Reinvention, 9(2),

It is well established in the literature that certain disease-associated gene signatures can be identified as a source for predicting the classification of samples or cell lines into diagnostic groups – for example, healthy and diseased. Using standa... Read More about The correlation threshold as a strategy for gene filtering, with application to irritable bowel syndrome and breast cancer microarray data.

Uncertainty of fast biological radiation dose assessment for emergency response scenarios (2016)
Journal Article
Ainsbury, E. A., Higueras, M., Puig, P., Einbeck, J., Samaga, D., Barquinero, J. F., …Woda, C. (2017). Uncertainty of fast biological radiation dose assessment for emergency response scenarios. International Journal of Radiation Biology, 93(1), 127-135. https://doi.org/10.1080/09553002.2016.1227106

Purpose: Reliable dose estimation is an important factor in appropriate dosimetric triage categorization of exposed individuals to support radiation emergency response. Materials and Methods: Following work done under the EU FP7 MULTIBIODOSE and RENE... Read More about Uncertainty of fast biological radiation dose assessment for emergency response scenarios.

k-Boxplots for mixture data (2016)
Journal Article
Qarmalah, N. M., Einbeck, J., & Coolen, F. P. (2018). k-Boxplots for mixture data. Statistical Papers, 59(2), 513-528. https://doi.org/10.1007/s00362-016-0774-7

This article introduces a new graphical tool to summarize data which possess a mixture structure. Computation of the required summary statistics makes use of posterior probabilities of class membership which can be obtained from a fitted mixture mode... Read More about k-Boxplots for mixture data.

Zero-inflated regression models for radiation-induced chromosome aberration data: A comparative study (2015)
Journal Article
Oliveira, M., Einbeck, J., Higueras, M., Ainsbury, E., Puig, P., & Rothkamm, K. (2016). Zero-inflated regression models for radiation-induced chromosome aberration data: A comparative study. Biometrical Journal, 58(2), 259-279. https://doi.org/10.1002/bimj.201400233

Within the field of cytogenetic biodosimetry, Poisson regression is the classical approach for modeling the number of chromosome aberrations as a function of radiation dose. However, it is common to find data that exhibit overdispersion. In practice,... Read More about Zero-inflated regression models for radiation-induced chromosome aberration data: A comparative study.

A summer with genes: Simple disease classification from microarray data (2015)
Journal Article
Einbeck, J., Jackson, S. E., & Kasim, A. (2015). A summer with genes: Simple disease classification from microarray data. Mathematics today, 51(4), 186-188

In this article we report on the work carried out within the framework of a summer project, part-funded by an IMA small grant, in which an undergraduate student (the second author of this manuscript) developed and implemented methodology for disease... Read More about A summer with genes: Simple disease classification from microarray data.

Implementation of a local principal curves algorithm for neutrino interaction reconstruction in a liquid argon volume (2014)
Journal Article
Back, J., Barker, G., Boyd, S., Einbeck, J., Haigh, M., Morgan, B., …Roythorne, D. (2014). Implementation of a local principal curves algorithm for neutrino interaction reconstruction in a liquid argon volume. The European Physical Journal C, 74(3), Article 2832. https://doi.org/10.1140/epjc/s10052-014-2832-4

A local principal curve algorithm has been implemented in three dimensions for automated track and shower reconstruction of neutrino interactions in a liquid argon time projection chamber. We present details of the algorithm and characterise its perf... Read More about Implementation of a local principal curves algorithm for neutrino interaction reconstruction in a liquid argon volume.

Some asymptotics for localized principal components and curves (2013)
Journal Article
Einbeck, J., & Zayed, M. (2014). Some asymptotics for localized principal components and curves. Communications in Statistics - Theory and Methods, 43(8), 1736-1749. https://doi.org/10.1080/03610926.2012.673676

The asymptotic behavior of localized principal components applying kernels as weights is investigated. In particular, we show that the first-order approximation of the first localized principal component at any given point only depends on the bandwid... Read More about Some asymptotics for localized principal components and curves.

Validation tests for semi-parametric models (2013)
Journal Article
Meintanis, S., & Einbeck, J. (2013). Validation tests for semi-parametric models. Journal of Statistical Computation and Simulation, 85(1), 131-146. https://doi.org/10.1080/00949655.2013.806922

Tests are proposed for validation of the hypothesis that a partial linear regression model adequately describes the structure of a given data set. The test statistics are formulated following the approach of Fourier-type conditional expectations firs... Read More about Validation tests for semi-parametric models.

Challenging the curse of dimensionality in multivariate local linear regression (2013)
Journal Article
Taylor, J., & Einbeck, J. (2013). Challenging the curse of dimensionality in multivariate local linear regression. Computational Statistics, 28(3), 955-976. https://doi.org/10.1007/s00180-012-0342-0

Local polynomial fitting for univariate data has been widely studied and discussed, but up until now the multivariate equivalent has often been deemed impractical, due to the so-called curse of dimensionality. Here, rather than discounting it complet... Read More about Challenging the curse of dimensionality in multivariate local linear regression.

A number-of-modes reference rule for density estimation under multimodality (2013)
Journal Article
Einbeck, J., & Taylor, J. (2013). A number-of-modes reference rule for density estimation under multimodality. Statistica Neerlandica, 67(1), 54-66. https://doi.org/10.1111/j.1467-9574.2012.00531.x

We consider kernel density estimation for univariate distributions. The question of interest is as follows: given that the data analyst has some background knowledge on the modality of the data (for instance, ‘data of this type are usually bimodal’),... Read More about A number-of-modes reference rule for density estimation under multimodality.

Goodness-of-fit tests in semi-linear models (2012)
Journal Article
Meintanis, S., & Einbeck, J. (2012). Goodness-of-fit tests in semi-linear models. Statistics and Computing, 22(4), 967-979. https://doi.org/10.1007/s11222-011-9266-8

Specification tests for the error distribution are proposed in semi-linear models, including the partial linear model and additive models. The tests utilize an integrated distance involving the empirical characteristic function of properly estimated... Read More about Goodness-of-fit tests in semi-linear models.

Using principal curves to analyse traffic patterns on freeways (2011)
Journal Article
Einbeck, J., & Dwyer, J. (2011). Using principal curves to analyse traffic patterns on freeways. Transportmetrica, 7(3), 229-246. https://doi.org/10.1080/18128600903500110

Scatterplots of traffic speed versus flow have caught considerable attention over the last decades due to their characteristic half-moon like shape. Modelling data of this type is difficult as both variables are actually not a function of each other... Read More about Using principal curves to analyse traffic patterns on freeways.

Bandwidth Selection for Mean-shift based Unsupervised Learning Techniques: a Unified Approach via Self-coverage (2011)
Journal Article
Einbeck, J. (2011). Bandwidth Selection for Mean-shift based Unsupervised Learning Techniques: a Unified Approach via Self-coverage. Journal of pattern recognition research, 6(2), 175-192. https://doi.org/10.13176/11.288

The mean shift is a simple but powerful tool emerging from the computer science literature which shifts a point to the local center of mass around this point. It has been used as a building block for several nonparametric unsupervised learning techni... Read More about Bandwidth Selection for Mean-shift based Unsupervised Learning Techniques: a Unified Approach via Self-coverage.

Data compression and regression through local principal curves and surfaces (2010)
Journal Article
Einbeck, J., Evers, L., & Powell, B. (2010). Data compression and regression through local principal curves and surfaces. International Journal of Neural Systems, 20(3), 177-192. https://doi.org/10.1142/s0129065710002346

We consider principal curves and surfaces in the context of multivariate regression modelling. For predictor spaces featuring complex dependency patterns between the involved variables, the intrinsic dimensionality of the data tends to be very small... Read More about Data compression and regression through local principal curves and surfaces.

Weighted Repeated Median Smoothing and Filtering (2007)
Journal Article
Fried, R., Einbeck, J., & Gather, U. (2007). Weighted Repeated Median Smoothing and Filtering. Journal of the American Statistical Association, 102(480), 1300-1308. https://doi.org/10.1198/016214507000001166

We propose weighted repeated median filters and smoothers for robust non-parametric regression in general and for robust online signal extraction from time series in particular. The new methods allow to remove outlying sequences and to preserve disco... Read More about Weighted Repeated Median Smoothing and Filtering.

A new package for fitting random effect models (2007)
Journal Article
Einbeck, J., Hinde, J., & Darnell, R. (2007). A new package for fitting random effect models. R news, 7(1), 26-30

Random effects have become a standard concept in statistical modelling over the last decades. They enter a wide range of applications by providing a simple tool to account for such problems as model misspecification, unobserved (latent) variables, un... Read More about A new package for fitting random effect models.

On design-weighted local fitting and its relation to the Horvitz-Thompson estimator (2007)
Journal Article
Einbeck, J., & Augustin, T. (2007). On design-weighted local fitting and its relation to the Horvitz-Thompson estimator. Statistica sinica, 19(1), 103-123

Weighting is a widely used concept in many fields of statistics and has frequently caused controversies on its justification and benefit. In this paper, we analyze design-weighted versions of the well-known local polynomial regression estimators, der... Read More about On design-weighted local fitting and its relation to the Horvitz-Thompson estimator.

Modelling beyond regression functions: An application of multimodal regression to speed-flow data (2006)
Journal Article
Einbeck, J., & Tutz, G. (2006). Modelling beyond regression functions: An application of multimodal regression to speed-flow data. Journal of the Royal Statistical Society: Series C, 55(4), 461-475. https://doi.org/10.1111/j.1467-9876.2006.00547.x

For speed–flow data, which are intensively discussed in transportation science, common nonparametric regression models of the type y=m(x)+noise turn out to be inadequate since simple functional models cannot capture the essential relationship between... Read More about Modelling beyond regression functions: An application of multimodal regression to speed-flow data.

A note on NPML estimation for exponential family regression models with unspecified dispersion parameter (2006)
Journal Article
Einbeck, J., & Hinde, J. (2006). A note on NPML estimation for exponential family regression models with unspecified dispersion parameter. Austrian Journal of Statistics, 35(2&3), 233-243

Nonparametric maximum likelihood (NPML) estimation for exponential families with unspecified dispersion parameter \phi suffers from computational instability, which can lead to highly fluctuating EM trajectories and suboptimal solutions, in particula... Read More about A note on NPML estimation for exponential family regression models with unspecified dispersion parameter.

Local fitting with a power basis (2004)
Journal Article
Einbeck, J. (2004). Local fitting with a power basis. Revstat Statistical Journal, 2(2), 102-126

Local polynomial modelling can be seen as a local fit of the data against a polynomial basis. In this paper we extend this method to the power basis, i.e. a basis which consists of the powers of an arbitrary function. Using an extended Taylor theorem... Read More about Local fitting with a power basis.

Local Smoothing with Robustness against outlying Predictors (2004)
Journal Article
Einbeck, J., Andre, C. D., & Singer, J. M. (2004). Local Smoothing with Robustness against outlying Predictors. Environmetrics, 15(6), 541-554. https://doi.org/10.1002/env.644

Outlying pollutant concentration data are frequently observed in time series studies conducted to investigate the effects of atmospheric pollution on mortality/morbidity. These outliers may severely affect the estimation procedures and even generate... Read More about Local Smoothing with Robustness against outlying Predictors.

A Simple Unifying Formula for Taylor's Theorem and Cauchy's Mean Value Theorem (2004)
Journal Article
Einbeck, J. (2004). A Simple Unifying Formula for Taylor's Theorem and Cauchy's Mean Value Theorem. International Journal of Pure and Applied Mathematics, 14(1), 69-74

We introduce a formula which generalizes Taylor's theorem from powers of linear terms z-x to functional terms \phi(z)-\phi(x), leading to a formula which reduces in a special case to Cauchy's generalized mean value theorem. In other words, regarding... Read More about A Simple Unifying Formula for Taylor's Theorem and Cauchy's Mean Value Theorem.

Online Monitoring with Local Smoothing Methods and Adaptive Ridging (2003)
Journal Article
Einbeck, J., & Kauermann, G. (2003). Online Monitoring with Local Smoothing Methods and Adaptive Ridging. Journal of Statistical Computation and Simulation, 73(12), 913-929. https://doi.org/10.1080/0094965031000104332

We consider online monitoring of sequentially arising data as e.g. met in clinical information systems. The general focus thereby is to detect breakpoints, i.e. timepoints where the measurement series suddenly changes the general level. The method su... Read More about Online Monitoring with Local Smoothing Methods and Adaptive Ridging.

Multivariate Local Fitting with General Basis Functions (2003)
Journal Article
Einbeck, J. (2003). Multivariate Local Fitting with General Basis Functions. Computational Statistics, 18(2), 185-203. https://doi.org/10.1007/s001800300140

In this paper we combine the concepts of local smoothing and fitting with basis functions for multivariate predictor variables. We start with arbitrary basis functions and show that the asymptotic variance at interior points is independent of the cho... Read More about Multivariate Local Fitting with General Basis Functions.