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Asymptotic and bootstrap properties of rank regressions

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  • Subbotin, Viktor

Abstract

The paper develops the bootstrap theory and extends the asymptotic theory of rank estimators, such as the Maximum Rank Correlation Estimator (MRC) of Han (1987), Monotone Rank Estimator (MR) of Cavanagh and Sherman (1998) or Pairwise-Difference Rank Estimators (PDR) of Abrevaya (2003). It is known that under general conditions these estimators have asymptotic normal distributions, but the asymptotic variances are difficult to find. Here we prove that the quantiles and the variances of the asymptotic distributions can be consistently estimated by the nonparametric bootstrap. We investigate the accuracy of inference based on the asymptotic approximation and the bootstrap, and provide bounds on the associated error. In the case of MRC and MR, the bound is a function of the sample size of order close to n^{-1/6}. The PDR estimators belong to a special subclass of rank estimators for which the bound is vanishing with the rate close to n^{-1/2}. The theoretical findings are illustrated with Monte-Carlo experiments and a real data example.

Suggested Citation

  • Subbotin, Viktor, 2007. "Asymptotic and bootstrap properties of rank regressions," MPRA Paper 9030, University Library of Munich, Germany, revised 20 Mar 2008.
  • Handle: RePEc:pra:mprapa:9030
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    File URL: https://mpra.ub.uni-muenchen.de/9030/1/MPRA_paper_9030.pdf
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    References listed on IDEAS

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    8. Abrevaya, Jason, 2003. "Pairwise-Difference Rank Estimation of the Transformation Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 437-447, July.
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    Cited by:

    1. Abby Alpert & David Powell, 2012. "Tax Elasticity of Labor Earnings for Older Individuals," Working Papers wp272, University of Michigan, Michigan Retirement Research Center.
    2. Jeremy T. Fox, 2008. "Estimating Matching Games with Transfers," NBER Working Papers 14382, National Bureau of Economic Research, Inc.
    3. Arkadiusz Szyd?owski, 2017. "Testing a parametric transformation model versus a nonparametric alternative," Discussion Papers in Economics 17/15, Department of Economics, University of Leicester.

    More about this item

    Keywords

    Rank Estimators; Bootstrap; M-Estimators; U-Statistics; U-Processes;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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