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Saddlepoint approximations and tests based on multivariate M-estimates

delete2003-08-01
delete36
delete
OA
AI
J
John Robinson *
E
Elvezio Ronchetti
G
G. A. Young
DOI：10.1214/aos/1059655909delete
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Abstract

Abstract

En 中文
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.
Keywords:
bootstrap tests
composite hypothesis
nonparametric likelihood
relative error
smooth functions of M-estimators
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Journal

Annals of Statistics cover
Annals of Statistics
IF:
3.7
Papers:
2.8K
Citations:
2.9W

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