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.
Publié le : 2003-08-14
Classification:
Bootstrap tests,
composite hypothesis,
nonparametric likelihood,
relative error,
smooth functions of $M$-estimators,
62F11,
62F05,
62G09
@article{1059655909,
author = {Robinson, J. and Ronchetti, E. and Young, G.A.},
title = {Saddlepoint approximations and tests based on multivariate M-estimates},
journal = {Ann. Statist.},
volume = {31},
number = {1},
year = {2003},
pages = { 1154-1169},
language = {en},
url = {http://dml.mathdoc.fr/item/1059655909}
}
Robinson, J.; Ronchetti, E.; Young, G.A. Saddlepoint approximations and tests based on multivariate M-estimates. Ann. Statist., Tome 31 (2003) no. 1, pp. 1154-1169. http://gdmltest.u-ga.fr/item/1059655909/