Saddlepoint approximations and tests based on multivariate M-estimates

• 成果类型: Article
• 署名作者: Robinson, J; Ronchetti, E; Young, GA
• 署名单位: University of Sydney; University of Geneva; University of Cambridge
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1059655909
• 发表日期: 2003
• 页码: 1154-1169
• 关键词: minimum contrast estimators; confidence-intervals; Empirical Likelihood; marginal densities; probabilities; bootstrap

摘要

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.