Consistency of the least median of squares estimator in nonlinear regression

Arnold J. Stromberg

doi:10.1080/03610929508831597

Consistency of the least median of squares estimator in nonlinear regression

Arnold J. Stromberg

Dr. Bing Zhang Department of Statistics

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

7 Scopus citations

Abstract

Recent research by Sakata and White (1995) presents the consistency and asymptotic normality of S-estimators in nonlinear regression. It is well known from research in linear regression that it is important to use a consistent high breakdown estimator as an initial estimate when computing an S-estimate. This paper presents the proof of the weak consistency of the least median of squares estimator in a nonlinear regression setting, thus suggesting that it is a reasonable choice for the starting value for computing S-estimates in nonlinear regression.

Original language	English
Pages (from-to)	1971-1984
Number of pages	14
Journal	Communications in Statistics - Theory and Methods
Volume	24
Issue number	8
DOIs	https://doi.org/10.1080/03610929508831597
State	Published - Jan 1 1995

Bibliographical note

Funding Information:
ACKNOWLEDGEMENTS This paper is a revision of a chapter of the authors Ph,D. dissertation from the University of North Carolina at Chapel ill. The author gratefully acknowledges the assistance of his advisor, Dawd Ruppert. lor this research was provided by KSF grant DMS-9204380 and NSA grant DA-904-92-H-3077.

Keywords

robust estimation

ASJC Scopus subject areas

Statistics and Probability

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10.1080/03610929508831597

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AB - Recent research by Sakata and White (1995) presents the consistency and asymptotic normality of S-estimators in nonlinear regression. It is well known from research in linear regression that it is important to use a consistent high breakdown estimator as an initial estimate when computing an S-estimate. This paper presents the proof of the weak consistency of the least median of squares estimator in a nonlinear regression setting, thus suggesting that it is a reasonable choice for the starting value for computing S-estimates in nonlinear regression.

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Consistency of the least median of squares estimator in nonlinear regression

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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