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August 2003 Saddlepoint approximations and tests based on multivariate M-estimates
J. Robinson, E. Ronchetti, G.A. Young
Ann. Statist. 31(4): 1154-1169 (August 2003). DOI: 10.1214/aos/1059655909

Abstract

We consider multidimensional M-functional parameters defined by expectations of score functions associated with multivariate M-estimators and tests for hypotheses concerning multidimensional smooth functions of these parameters. We propose a test statistic suggested by the exponent in the saddlepoint approximation to the density of the function of the M-estimates. This statistic is analogous to the log likelihood ratio in the parametric case. We show that this statistic is approximately distributed as a chi-squared variate and obtain a Lugannani-Rice style adjustment giving a relative error of order $n^{-1}$. We propose an empirical exponential likelihood statistic and consider a test based on this statistic. Finally we present numerical results for three examples including one in robust regression.

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J. Robinson. E. Ronchetti. G.A. Young. "Saddlepoint approximations and tests based on multivariate M-estimates." Ann. Statist. 31 (4) 1154 - 1169, August 2003. https://doi.org/10.1214/aos/1059655909

Information

Published: August 2003
First available in Project Euclid: 31 July 2003

zbMATH: 1056.62023
MathSciNet: MR2001646
Digital Object Identifier: 10.1214/aos/1059655909

Subjects:
Primary: 62F05, 62F11
Secondary: 62G09

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 4 • August 2003
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