Huber-sense robust M-estimation of a scale parameter, with application to the exponential distribution

Peter F. Thall

doi:10.1080/01621459.1979.10481631

Huber-sense robust M-estimation of a scale parameter, with application to the exponential distribution

Peter F. Thall

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

10 Scopus citations

Abstract

Huber’s (1964) classical theory of robust M-estimation of a location parameter is also applicable to nonnegative data X having scale parameter θ, since Y = log X has location parameter log θ. In the present article, Huber’s location parameter results are reformulated in the scale parameter context and then applied to the problem of robust estimation of the parameter of the exponential distribution. The robust M-estimator is obtained here as the solution of a minimax problem, and it turns out to be a type of Winsorized mean.

Original language	English (US)
Pages (from-to)	147-152
Number of pages	6
Journal	Journal of the American Statistical Association
Volume	74
Issue number	365
DOIs	https://doi.org/10.1080/01621459.1979.10481631
State	Published - Mar 1979
Externally published	Yes

Keywords

Exponential distribution
M-estimation
Minimax
Robust statistics
Scale parameter

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1080/01621459.1979.10481631

Cite this

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title = "Huber-sense robust M-estimation of a scale parameter, with application to the exponential distribution",

abstract = "Huber{\textquoteright}s (1964) classical theory of robust M-estimation of a location parameter is also applicable to nonnegative data X having scale parameter θ, since Y = log X has location parameter log θ. In the present article, Huber{\textquoteright}s location parameter results are reformulated in the scale parameter context and then applied to the problem of robust estimation of the parameter of the exponential distribution. The robust M-estimator is obtained here as the solution of a minimax problem, and it turns out to be a type of Winsorized mean.",

keywords = "Exponential distribution, M-estimation, Minimax, Robust statistics, Scale parameter",

author = "Thall, {Peter F.}",

note = "Funding Information: .. Peter F. Thall is Assistant Professor, Programs in Mathematical Sciences, The University of Texas at Dallas, Richardson, TX 75080. Research was partially supported by Office of Naval Research contract No. NOOO14-76-C-0608. The author gratefully acknowledges the guidance and encouragement of his advisor, R.J. Serfling. The author is also indebted to the referee for many detailed comments and suggestions, which led to a substantial improvement of the manuscript.",

year = "1979",

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doi = "10.1080/01621459.1979.10481631",

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AU - Thall, Peter F.

N1 - Funding Information: .. Peter F. Thall is Assistant Professor, Programs in Mathematical Sciences, The University of Texas at Dallas, Richardson, TX 75080. Research was partially supported by Office of Naval Research contract No. NOOO14-76-C-0608. The author gratefully acknowledges the guidance and encouragement of his advisor, R.J. Serfling. The author is also indebted to the referee for many detailed comments and suggestions, which led to a substantial improvement of the manuscript.

PY - 1979/3

Y1 - 1979/3

N2 - Huber’s (1964) classical theory of robust M-estimation of a location parameter is also applicable to nonnegative data X having scale parameter θ, since Y = log X has location parameter log θ. In the present article, Huber’s location parameter results are reformulated in the scale parameter context and then applied to the problem of robust estimation of the parameter of the exponential distribution. The robust M-estimator is obtained here as the solution of a minimax problem, and it turns out to be a type of Winsorized mean.

AB - Huber’s (1964) classical theory of robust M-estimation of a location parameter is also applicable to nonnegative data X having scale parameter θ, since Y = log X has location parameter log θ. In the present article, Huber’s location parameter results are reformulated in the scale parameter context and then applied to the problem of robust estimation of the parameter of the exponential distribution. The robust M-estimator is obtained here as the solution of a minimax problem, and it turns out to be a type of Winsorized mean.

KW - Exponential distribution

KW - M-estimation

KW - Minimax

KW - Robust statistics

KW - Scale parameter

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JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

IS - 365

ER -

Huber-sense robust M-estimation of a scale parameter, with application to the exponential distribution

Abstract

Keywords

ASJC Scopus subject areas

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