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Original title:
A Nonparametric Bootstrap Comparison of Variances of Robust Regression Estimators.
Authors: Kalina, Jan ; Tobišková, Nicole ; Tichavský, Jan
Document type: Papers
Conference/Event: MME 2019: International Conference on Mathematical Methods in Economics /37./, České Budějovice (CZ), 20190911
Year: 2019
Language: eng
Abstract: While various robust regression estimators are available for the standard linear regression model, performance comparisons of individual robust estimators over real or simulated datasets seem to be still lacking. In general, a reliable robust estimator of regression parameters should be consistent and at the same time should have a relatively small variability, i.e. the variances of individual regression parameters should be small. The aim of this paper is to compare the variability of S-estimators, MM-estimators, least trimmed squares, and least weighted squares estimators. While they all are consistent under general assumptions, the asymptotic covariance matrix of the least weighted squares remains infeasible, because the only available formula for its computation depends on the unknown random errors. Thus, we take resort to a nonparametric bootstrap comparison of variability of different robust regression estimators. It turns out that the best results are obtained either with MM-estimators, or with the least weighted squares with suitable weights. The latter estimator is especially recommendable for small sample sizes.
Keywords: bootstrap; least weighted squares; linear regression; outliers; robustness
Project no.: GA19-05704S (CEP), GA17-01251S (CEP)
Funding provider: GA ČR, GA ČR
Host item entry: Conference Proceedings. 37th International Conference on Mathematical Methods in Economics 2019, ISBN 978-80-7394-760-6
Institution: Institute of Computer Science AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: https://mme2019.ef.jcu.cz/files/conference_proceedings.pdf
Original record: http://hdl.handle.net/11104/0300321
Permalink: http://www.nusl.cz/ntk/nusl-403664
The record appears in these collections:
Research > Institutes ASCR > Institute of Computer Science
Conference materials > Papers
Authors: Kalina, Jan ; Tobišková, Nicole ; Tichavský, Jan
Document type: Papers
Conference/Event: MME 2019: International Conference on Mathematical Methods in Economics /37./, České Budějovice (CZ), 20190911
Year: 2019
Language: eng
Abstract: While various robust regression estimators are available for the standard linear regression model, performance comparisons of individual robust estimators over real or simulated datasets seem to be still lacking. In general, a reliable robust estimator of regression parameters should be consistent and at the same time should have a relatively small variability, i.e. the variances of individual regression parameters should be small. The aim of this paper is to compare the variability of S-estimators, MM-estimators, least trimmed squares, and least weighted squares estimators. While they all are consistent under general assumptions, the asymptotic covariance matrix of the least weighted squares remains infeasible, because the only available formula for its computation depends on the unknown random errors. Thus, we take resort to a nonparametric bootstrap comparison of variability of different robust regression estimators. It turns out that the best results are obtained either with MM-estimators, or with the least weighted squares with suitable weights. The latter estimator is especially recommendable for small sample sizes.
Keywords: bootstrap; least weighted squares; linear regression; outliers; robustness
Project no.: GA19-05704S (CEP), GA17-01251S (CEP)
Funding provider: GA ČR, GA ČR
Host item entry: Conference Proceedings. 37th International Conference on Mathematical Methods in Economics 2019, ISBN 978-80-7394-760-6
Institution: Institute of Computer Science AS ČR (web)
Document availability information: Fulltext is available at external website.
External URL: https://mme2019.ef.jcu.cz/files/conference_proceedings.pdf
Original record: http://hdl.handle.net/11104/0300321
Permalink: http://www.nusl.cz/ntk/nusl-403664
The record appears in these collections:
Research > Institutes ASCR > Institute of Computer Science
Conference materials > Papers
Record created 2019-10-19, last modified 2023-12-06