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A note on robust estimation in logistic regression model

100%
Bednarski T.
Discussiones Mathematicae Probability and Statistics
|
2016
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tom 36
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nr 1-2
43-51
EN
Computationally attractive Fisher consistent robust estimation methods based on adaptive explanatory variables trimming are proposed for the logistic regression model. Results of a Monte Carlo experiment and a real data analysis show its good behavior for moderate sample sizes. The method is applicable when some distributional information about explanatory variables is available.
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On inconsistency of Hellwig's variable choice method in regression models

63%
Bednarski T., Borowicz F.
Discussiones Mathematicae Probability and Statistics
|
2009
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tom 29
|
nr 1
41-51
EN
It is shown that a popular variable choice method of Hellwig, which is recommended in the Polish econometric textbooks does not enjoy a very basic consistency property. It means in particular that the method may lead to rejection of significant variables in econometric modeling. A simulation study and a real data analysis case are given to support theoretical results.
3
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On a robust significance test for the Cox regression model

63%
Bednarski T., Borowicz F.
Discussiones Mathematicae Probability and Statistics
|
2006
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tom 26
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nr 2
221-233
EN
A robust significance testing method for the Cox regression model, based on a modified Wald test statistic, is discussed. Using Monte Carlo experiments the asymptotic behavior of the modified robust versions of the Wald statistic is compared with the standard significance test for the Cox model based on the log likelihood ratio test statistic.
4
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Adaptive trimmed likelihood estimation in regression

51%
Bednarski T., Clarke B., Schubert D.
Discussiones Mathematicae Probability and Statistics
|
2010
|
tom 30
|
nr 2
203-219
EN
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 robust estimator such as the least median of squares (LMS) or least trimmed squares (LTS) or for example the more recent MM estimators of Yohai. Such estimators are now standard in statistics computing packages, for example as in SPLUS or R. In addition to the asymptotics we provide data analyses supporting the new adaptive approach. This approach appears to work well on a number of data sets and is quicker than the related brute force adaptive regression approach described in Clarke (2000). This current approach builds on the work of Bednarski and Clarke (2002) which considered the asymptotics for the location estimator only.
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