Robinson, J. Ronchetti, Elvezio Young, G. A. 2003 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. application/pdf https://localhost:5000/ark:/12658/srd1317931 https://susi.usi.ch/global/documents/317931 https://susi.usi.ch/documents/317931/files/ronchetti_AS_2003.pdf eng http://links.jstor.org/sici?sici=0090-5364%28200308%2931%3A4%3C1154%3ASAATBO%3E2.0.CO%3B2-5 info:eu-repo/semantics/altIdentifier/ark/12658/srd1317931 info:eu-repo/semantics/openAccess License undefined The Annals of Statistics. - Institute of Mathematical Statistics. - 2003, vol. 31, no. 4, p. 1154-1169 info:eu-repo/classification/udc/33 Saddlepoint approximations and tests based on multivariate M-estimates http://purl.org/coar/resource_type/c_6501