Open Access
Translator Disclaimer
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


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.


Download Citation

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


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

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

Primary: 62F05 , 62F11
Secondary: 62G09

Keywords: Bootstrap tests , composite hypothesis , nonparametric likelihood , relative error , smooth functions of $M$-estimators

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 4 • August 2003
Back to Top