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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.

Generative linear mixture modelling (2012)
Presentation / Conference Contribution
Lawson, A., & Einbeck, J. (2012). Generative linear mixture modelling. In A. Komarek, & S. Nagy (Eds.), 27th International Workshop on Statistical Modelling, 16-20 July 2012, Prague, Czech Republic ; proceedings (595-600)

For multivariate data with a low–dimensional latent structure, a novel approach to linear dimension reduction based on Gaussian mixture models is pro- posed. A generative model is assumed for the data, where the mixture centres (or ‘mass points’) are... Read More about Generative linear mixture modelling.

Penalized regression on principal manifolds with application to combustion modelling (2012)
Presentation / Conference Contribution
Einbeck, J., Isaac, B., Evers, L., & Parente, A. (2012). Penalized regression on principal manifolds with application to combustion modelling. In A. Komarek, & S. Nagy (Eds.), 27th International Workshop on Statistical Modelling, 16-20 July 2012, Prague, Czech Republic ; proceedings (117-122)

For multivariate regression problems featuring strong and non–linear dependency patterns between the involved predictors, it is attractive to reduce the dimension of the estimation problem by approximating the predictor space through a principal surf... Read More about Penalized regression on principal manifolds with application to combustion modelling.

Multivariate regression smoothing through the 'fallling net' (2011)
Presentation / Conference Contribution
Taylor, J., & Einbeck, J. (2011). Multivariate regression smoothing through the 'fallling net'. In D. Conesa, A. Forte, A. Lopez-Quilez, & F. Munoz (Eds.), 26th International Workshop on Statistical Modelling, 5-11 July 2011, Valencia, Spain ; proceedings (597-602)

We consider multivariate regression smoothing through a conditional mean shift procedure. By computing local conditional means iteratively over a set or grid of target points, at each iteration a `net' is formed which gently drifts towards the data c... Read More about Multivariate regression smoothing through the 'fallling net'.

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.

Constructing Economic Summary Indexes via Principal Curves (2010)
Presentation / Conference Contribution
Zayed, M., & Einbeck, J. (2010). Constructing Economic Summary Indexes via Principal Curves. In Y. Lechevallier, & G. Saporta (Eds.),

Index number construction is an important and traditional subject in both the statistical and the economical sciences. A novel technique based on localized principal components to compose a single summary index from a collection of indexes is propose... Read More about Constructing Economic Summary Indexes via Principal Curves.

Localized regression on principal manifolds (2010)
Presentation / Conference Contribution
Einbeck, J., & Evers, L. (2010). Localized regression on principal manifolds. In A. Bowman (Ed.),

We consider nonparametric dimension reduction techniques for multivariate regression problems in which the variables constituting the predictor space are strongly nonlinearly related. Specifically, the predictor space is approximated via ``local'' pr... Read More about Localized regression on principal manifolds.

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.

Data compression and regression based on local principal curves (2010)
Presentation / Conference Contribution
Einbeck, J., Evers, L., & Hinchliff, K. (2010). Data compression and regression based on local principal curves. In A. Fink, B. Lausen, W. Seidel, & A. Ultsch (Eds.), Advances in data analysis, data handling and business intelligence (701-712). https://doi.org/10.1007/978-3-642-01044-6_64

Frequently the predictor space of a multivariate regression problem of the type y = m(x_1, …, x_p ) + ε is intrinsically one-dimensional, or at least of far lower dimension than p. Usual modeling attempts such as the additive model y = m_1(x_1) + … +... Read More about Data compression and regression based on local principal curves.

Representing complex data using localized principal components with application to astronomical data. (2008)
Book Chapter
Einbeck, J., Evers, L., & Bailer-Jones, C. (2008). Representing complex data using localized principal components with application to astronomical data. In A. Gorban, B. Kegl, D. Wunsch, & A. Zinovyev (Eds.), Lecture Notes in Computational Science and Engineering (180-204). Springer Verlag. https://doi.org/10.1007/978-3-540-73750-6_7

Often the relation between the variables constituting a multivariate data space might be characterized by one or more of the terms: ``nonlinear'', ``branched'', ``disconnected'', ``bended'', ``curved'', ``heterogeneous'', or, more general, ``complex'... Read More about Representing complex data using localized principal components with application to astronomical data..

League tables for literacy survey data based on random effect models (2008)
Presentation / Conference Contribution
Sofroniou, N., Hoad, D., & Einbeck, J. (2008). League tables for literacy survey data based on random effect models. In P. Eilers (Ed.), 23rd International Workshop on Statistical Modelling, 7-11 July 2008, Utrecht ; proceedings (402-405)

Data from the International Adult Literacy Survey are used to illustrate how league tables can be obtained from summary data, consisting of percentages and their standard errors, using random effects models estimated by nonparametric maximum likeliho... Read More about League tables for literacy survey data based on random effect models.

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 comparative study of nonparametric derivative estimators. (2007)
Presentation / Conference Contribution
Newell, J., & Einbeck, J. (2007). A comparative study of nonparametric derivative estimators. In J. del Castillo, A. Espinal, & P. Puig (Eds.),

Nonparametric derivative estimation has never attracted much attention as one gets the derivative estimates as ``by-products'' from a local polynomial or spline fit. However, these estimates often suffer from boundary effects and are very sensitive t... Read More about A comparative study of nonparametric derivative estimators..

Smoothing, Sampling, and Basu's elephants (2007)
Presentation / Conference Contribution
Einbeck, J., Augustin, T., & Singer, J. M. (2007). Smoothing, Sampling, and Basu's elephants. In J. del Castillo, A. Espinal, & P. Puig (Eds.),

We investigate design-weighted local smoothing and show that the optimal (bias-minimizing) weights have similar form and interpretation as the optimal weights given by the Horvitz-Thompson theorem known from sampling theory. We set forth that the haz... Read More about Smoothing, Sampling, and Basu's elephants.

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.