Saddlepoint approximations for multivariate M -estimates with applications to bootstrap accuracy

Field, Chris; Robinson, John; Ronchetti, Elvezio

doi:10.1007/s10463-006-0083-3

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Journal article

Saddlepoint approximations for multivariate M -estimates with applications to bootstrap accuracy

Field, Chris Department of Mathematics and Statistics, Dalhousie University, Halifax, Canada
Robinson, John School of Mathematics and Statistics, University of Sydney, Sydney, Australia
Ronchetti, Elvezio Istituto di finanza (IFin), Facoltà di scienze economiche, Università della Svizzera italiana, Svizzera

2008

Published in:

Annals of the Institute of Statistical Mathematics. - Springer Netherlands. - 2008, vol. 60, no. 1, p. 205-224

English We obtain marginal tail area approximations for the one-dimensional test statistic based on the appropriate component of the M-estimate for both standardized and Studentized versions which are needed for tests and confidence intervals. The result is proved under conditions which allow the application to finite sample situations such as the bootstrap and involves a careful discretization with saddlepoints being used for each neighbourhood. These results are used to obtain second-order relative error results on the accuracy of the Studentized and the tilted bootstrap. The tail area approximations are applied to a Poisson regression model and shown to have very good accuracy.

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