Consistency of the least median of squares estimator in nonlinear regression

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7 Scopus citations


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 languageEnglish
Pages (from-to)1971-1984
Number of pages14
JournalCommunications in Statistics - Theory and Methods
Issue number8
StatePublished - 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.


  • robust estimation

ASJC Scopus subject areas

  • Statistics and Probability


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