High-order asymptotic expansions for robust tests

De Rossi, François-Xavier ; Gatto, Riccardo

In: Biometrika, 2001, vol. 88, no. 4, p. 1153-1168

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    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