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Extensions of the Markov chain marginal bootstrap

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  • Kocherginsky, Masha
  • He, Xuming
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    Abstract

    The Markov chain marginal bootstrap (MCMB) was introduced by He and Hu [2002. Markov chain marginal bootstrap. J. Amer. Statist. Assoc. 97(459) (2002) 783-795] as a bootstrap-based method for constructing confidence intervals or regions for a wide class of M-estimators in linear regression and maximum likelihood estimators in certain parametric models. In this article we discuss more general applications of MCMB-A, an extension of the MCMB algorithm, which was first proposed in Kocherginsky et al. [2005. Practical confidence intervals for regression quantiles. J. Comput. Graphical Statist. 14, 41-55] for quantile regression models. We also present a further extension of the MCMB algorithm, the B-transformation, which is a transformation of the estimating equations, aiming to broaden the applicability of the MCMB algorithm to general estimating equations that are not necessarily likelihood-based. We show that applying the A- and B-transformations jointly enables the MCMB algorithm to be used for inference related to a very general class of estimating equations. We illustrate the use of the MCMB-AB algorithm with a nonlinear regression model with heteroscedastic error distribution.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 77 (2007)
    Issue (Month): 12 (July)
    Pages: 1258-1268

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    Handle: RePEc:eee:stapro:v:77:y:2007:i:12:p:1258-1268

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    Related research

    Keywords: Bootstrap General estimating equations Confidence intervals Transformation Nonlinear regression;

    References

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    1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    2. He X. & Hu F., 2002. "Markov Chain Marginal Bootstrap," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 783-795, September.
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