Robust estimators and their relations
J. Jurečková (1983)
Acta Universitatis Carolinae. Mathematica et Physica
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J. Jurečková (1983)
Acta Universitatis Carolinae. Mathematica et Physica
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Norbert Stockinger, Rudolf Dutter (1987)
Kybernetika
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Irène Gijbels (2008)
Applications of Mathematics
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For nonparametric estimation of a smooth regression function, local linear fitting is a widely-used method. The goal of this paper is to briefly review how to use this method when the unknown curve possibly has some irregularities, such as jumps or peaks, at unknown locations. It is then explained how the same basic method can be used when estimating unsmooth probability densities and conditional variance functions.
Nicholas T. Longford (2008)
SORT
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The one-way analysis of variance is a staple of elementary statistics courses. The hypothesis test of homogeneity of the means encourages the use of the selected-model based estimators which are usually assessed without any regard for the uncertainty about the outcome of the test. We expose the weaknesses of such estimators when the uncertainty is taken into account, as it should be, and propose synthetic estimators as an alternative.
Tadeusz Bednarski, Brenton R. Clarke, Daniel Schubert (2010)
Discussiones Mathematicae Probability and Statistics
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In this paper we derive an asymptotic normality result for an adaptive trimmed likelihood estimator of regression starting from initial high breakdownpoint robust regression estimates. The approach leads to quickly and easily computed robust and efficient estimates for regression. A highlight of the method is that it tends automatically in one algorithm to expose the outliers and give least squares estimates with the outliers removed. The idea is to begin with a rapidly computed consistent...
Vassiliy G. Voinov, Mikhail S. Nikulin (1995)
Qüestiió
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Since 1956, a large number of papers have been devoted to Stein's technique of obtaining improved estimators of parameters, for several statistical models. We give a brief review of these papers, emphasizing those aspects which are interesting from the point of view of the theory of unbiased estimation.