The use and interpretation of residuals based on Robust estimation

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

doi:10.1080/01621459.1993.10476406

The use and interpretation of residuals based on Robust estimation

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

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

51 Scopus citations

Abstract

Residual plots and diagnostic techniques are important tools for examining the fit of a regression model. In the case of least squares fits, plots of residuals provide a visual assessment of the adequacy of various aspects of the fitted model. An important question is whether plots of robust residuals can be interpreted in the same manner as their least squares counterparts. This article addresses this problem for two popular classes of robust estimates: M estimates and GM estimates of the Mallows and Schweppe types. First-order properties of the residuals and fitted values are derived under correct and misspecified models. These properties are insightful on the general interpretability of robust residual plots and on their ability to detect curvature in misspecified models. The results of a simulation study consisting of tests for randomness and curvature in residual plots supports these theoretical properties. Standardization of robust residuals is also presented.

Original language	English
Pages (from-to)	1254-1263
Number of pages	10
Journal	Journal of the American Statistical Association
Volume	88
Issue number	424
DOIs	https://doi.org/10.1080/01621459.1993.10476406
State	Published - Dec 1993

Bibliographical note

Funding Information:
* Joseph W. McKean is Professor of Statistics, Depktment of Mathematics and Statistics, Western Michigan University, Kalamazoo, MI 49008. Simon J. Sheather is Senior Lecturer, Australian Graduate School of Management, University of New South Wales, Kensington, NSW, 2033, Australia. Thomas P. Hettmansperger is Professor of Statistics, Department of Statistics, Penn- sylvania State University, University Park, PA 16802. McKean’s research was partially supported by National Science Foundation Grant DMS- 9 1039 16; Sheather’s research was partially supported by grant support from the Australian Research Council; and Hettmansperger’s research was partially supported by National Science Foundation Grant DMS-9100228 AOI. The authors thank the referees for helpful comments on an earlier version of this article.

Keywords

GM estimate
High breakdown
Linear model
M estimate
Regression diagnostic
Residual plot

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1080/01621459.1993.10476406

Cite this

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title = "The use and interpretation of residuals based on Robust estimation",

abstract = "Residual plots and diagnostic techniques are important tools for examining the fit of a regression model. In the case of least squares fits, plots of residuals provide a visual assessment of the adequacy of various aspects of the fitted model. An important question is whether plots of robust residuals can be interpreted in the same manner as their least squares counterparts. This article addresses this problem for two popular classes of robust estimates: M estimates and GM estimates of the Mallows and Schweppe types. First-order properties of the residuals and fitted values are derived under correct and misspecified models. These properties are insightful on the general interpretability of robust residual plots and on their ability to detect curvature in misspecified models. The results of a simulation study consisting of tests for randomness and curvature in residual plots supports these theoretical properties. Standardization of robust residuals is also presented.",

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doi = "10.1080/01621459.1993.10476406",

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N2 - Residual plots and diagnostic techniques are important tools for examining the fit of a regression model. In the case of least squares fits, plots of residuals provide a visual assessment of the adequacy of various aspects of the fitted model. An important question is whether plots of robust residuals can be interpreted in the same manner as their least squares counterparts. This article addresses this problem for two popular classes of robust estimates: M estimates and GM estimates of the Mallows and Schweppe types. First-order properties of the residuals and fitted values are derived under correct and misspecified models. These properties are insightful on the general interpretability of robust residual plots and on their ability to detect curvature in misspecified models. The results of a simulation study consisting of tests for randomness and curvature in residual plots supports these theoretical properties. Standardization of robust residuals is also presented.

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The use and interpretation of residuals based on Robust estimation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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