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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.