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Bootstrap Approximation to the Distribution of M-estimates in a Linear Model

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Abstract

The authors establish the approximations to the distribution of M-estimates in a linear model by the bootstrap and the linear representation of bootstrap M-estimation, and prove that the approximation is valid in probability 1. A simulation is made to show the effects of bootstrap approximation, randomly weighted approximation and normal approximation.

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Authors and Affiliations

  1. Department of Statistics, Shanghai University of Finance and Economics, Shanghai, 200433, P. R. China

    Xiao Ming Wang

  2. Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong

    Wang Zhou

Authors
  1. Xiao Ming Wang
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  2. Wang Zhou
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Correspondence to Xiao Ming Wang.

Additional information

This work is supported by Fund of 211 Program of SHUFE and Fund of Educational Committee of Shanghai

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Wang, X.M., Zhou, W. Bootstrap Approximation to the Distribution of M-estimates in a Linear Model. Acta Math Sinica 20, 93–104 (2004). https://doi.org/10.1007/s10114-003-0246-6

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  • DOI: https://doi.org/10.1007/s10114-003-0246-6

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