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

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An Erratum to this article was published on 22 December 2006

Abstract

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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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada, B3H 3J5

    Chris Field

  2. School of Mathematics and Statistics, University of Sydney, NSW, Sydney, 2006, Australia

    John Robinson

  3. Department of Econometrics, University of Geneva, Geneva, Switzerland

    Elvezio Ronchetti

Authors
  1. Chris Field
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  2. John Robinson
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  3. Elvezio Ronchetti
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Corresponding author

Correspondence to John Robinson.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s10463-006-0101-5

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Field, C., Robinson, J. & Ronchetti, E. Saddlepoint approximations for multivariate M-estimates with applications to bootstrap accuracy. AISM 60, 205–224 (2008). https://doi.org/10.1007/s10463-006-0083-3

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  • DOI: https://doi.org/10.1007/s10463-006-0083-3

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