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Biometrika 2001 88(4):1153-1168; doi:10.1093/biomet/88.4.1153
© 2001 by Biometrika Trust
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High-order asymptotic expansions for robust tests

François-Xavier De Rossi1 and Riccardo Gatto2

1 Swiss Federal Statistical Office, 2010 Neuchâtel, Switzerland francois-xavier.derossi{at}bfs.admin.ch 2 Institut für Mathematische Statistik und Versicherungslehre, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland gatto{at}stat.unibe.ch

This paper provides high-order asymptotic expansions for the M-ratio and the signed-root M-ratio robust test statistics, which allow one to compute accurate approximations to significance or critical values using the Edgeworth approximation, the Bartlett correction, the variance correction or the saddlepoint approximation. Specific results are obtained for the linear regression model with the Huber M-estimator.A Monte Carlo study illustrates the numerical accuracy of these approximations, with respect to the usual first-order approximations.

Key Words: Bartlett correction; Edgeworth approximation; Likelihood ratio test; M-ratio test; Nuisance parameter; Regression model; Robust p-value and quantile; Saddlepoint approximation; Signed-root likelihood ratio test; Signed-root M-ratio test

Received January 1999. Revised March 2001


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