Asymptotic and bootstrap properties of rank regressions

Viktor Subbotin

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Rank Estimators; Bootstrap; M-Estimators; U-Statistics; U-Processes (search for similar items in EconPapers)
JEL-codes: C12 C14 C15 (search for similar items in EconPapers)
Date: 2007-11-08, Revised 2008-03-20
New Economics Papers: this item is included in nep-dcm, nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:9030

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