Robust and high-breakdown fits of polynomial models

Joseph W. McKean; Simon J. Sheather; Thomas P. Hettmansperger

doi:10.1080/00401706.1994.10485847

Robust and high-breakdown fits of polynomial models

Joseph W. McKean, Simon J. Sheather, Thomas P. Hettmansperger

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

A common strategy for fitting a polynomial regression model is to use a combination of residual plots and significance tests on the regression coefficients. In this article, we consider whether this strategy can be used effectively for fits based on two classes of robust estimatesnamely—M estimates and GM estimates. We show that the asymptotic relative efficiency of Mallows-type high-breakdown GM estimates can be quite low for detecting curvature in polynomial models. Furthermore, the GM-residual plots may also be of little help in detecting curvature. An example and a simulation study illustrate the discussion.

Original language	English
Pages (from-to)	409-415
Number of pages	7
Journal	Technometrics
Volume	36
Issue number	4
DOIs	https://doi.org/10.1080/00401706.1994.10485847
State	Published - Nov 1994

Bibliographical note

Funding Information:
The work of Joseph W. McKean was partially supported by National Science Foundation Grant DMS-9103916,t he work of Simon J. Sheather was partially supported by the Australian Research Council, and the work of Thomas P. Hettmansperger was partially supported by National Science Foundation Grant DMS-9100228 AOl. We thank anonymous referees for helpful comments on an earlier version of this article.

Keywords

GM estimate
Linear model
M estimate
Residual plot
Robust

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
Applied Mathematics

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10.1080/00401706.1994.10485847

Cite this

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title = "Robust and high-breakdown fits of polynomial models",

abstract = "A common strategy for fitting a polynomial regression model is to use a combination of residual plots and significance tests on the regression coefficients. In this article, we consider whether this strategy can be used effectively for fits based on two classes of robust estimatesnamely—M estimates and GM estimates. We show that the asymptotic relative efficiency of Mallows-type high-breakdown GM estimates can be quite low for detecting curvature in polynomial models. Furthermore, the GM-residual plots may also be of little help in detecting curvature. An example and a simulation study illustrate the discussion.",

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AU - Sheather, Simon J.

AU - Hettmansperger, Thomas P.

N1 - Funding Information: The work of Joseph W. McKean was partially supported by National Science Foundation Grant DMS-9103916,t he work of Simon J. Sheather was partially supported by the Australian Research Council, and the work of Thomas P. Hettmansperger was partially supported by National Science Foundation Grant DMS-9100228 AOl. We thank anonymous referees for helpful comments on an earlier version of this article.

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N2 - A common strategy for fitting a polynomial regression model is to use a combination of residual plots and significance tests on the regression coefficients. In this article, we consider whether this strategy can be used effectively for fits based on two classes of robust estimatesnamely—M estimates and GM estimates. We show that the asymptotic relative efficiency of Mallows-type high-breakdown GM estimates can be quite low for detecting curvature in polynomial models. Furthermore, the GM-residual plots may also be of little help in detecting curvature. An example and a simulation study illustrate the discussion.

AB - A common strategy for fitting a polynomial regression model is to use a combination of residual plots and significance tests on the regression coefficients. In this article, we consider whether this strategy can be used effectively for fits based on two classes of robust estimatesnamely—M estimates and GM estimates. We show that the asymptotic relative efficiency of Mallows-type high-breakdown GM estimates can be quite low for detecting curvature in polynomial models. Furthermore, the GM-residual plots may also be of little help in detecting curvature. An example and a simulation study illustrate the discussion.

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KW - Linear model

KW - M estimate

KW - Residual plot

KW - Robust

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Robust and high-breakdown fits of polynomial models

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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