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February 2000 The density of multivariate $M$-estimates
Anthony Almudevar, Chris Field, John Robinson
Ann. Statist. 28(1): 275-297 (February 2000). DOI: 10.1214/aos/1016120373


When a unique $M$-estimate exists, its density is obtained as a corollary to a more general theorem which asserts that under mild conditions the intensity function of the point process of solutions of the estimating equations exists and is given by the density of the estimating function standardized by multiplying it by the inverse of its derivative. We apply the results to give a result for Huber’s proposal 2 applied to regression and scale estimates. We also give a saddlepoint approximation for the density and use this to give approximations for tail areas for smooth functions of the $M$-estimates.


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Anthony Almudevar. Chris Field. John Robinson. "The density of multivariate $M$-estimates." Ann. Statist. 28 (1) 275 - 297, February 2000.


Published: February 2000
First available in Project Euclid: 14 March 2002

zbMATH: 1106.62335
MathSciNet: MR1762912
Digital Object Identifier: 10.1214/aos/1016120373

Primary: 62E17
Secondary: 60G55 , 62F11

Keywords: $M$-estimator , intensity , point process

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 1 • February 2000
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