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Saddlepoint approximations and tests based on multivariate M -estimates

Robinson, J.
Young, G.A.
Published in Annals of statistics. 2003, vol. 31, no. 4, p. 1154-1169
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 . 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 testsComposite hypothesisNonparametric likelihoodRelative errorSmooth functions of M-estimators
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ROBINSON, J., RONCHETTI, Elvezio, YOUNG, G.A. Saddlepoint approximations and tests based on multivariate M -estimates. In: Annals of statistics, 2003, vol. 31, n° 4, p. 1154-1169. doi: 10.1214/aos/1059655909 https://archive-ouverte.unige.ch/unige:22941

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Deposited on : 2012-09-18

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