Asymptotic and Bootstrap Properties of Rank Regressions

61 Pages Posted: 12 Nov 2007

See all articles by Viktor Subbotin

Viktor Subbotin

Department of Economics, Northwestern University

Date Written: November 2007

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

JEL Classification: C12, C14

Suggested Citation

Subbotin, Viktor, Asymptotic and Bootstrap Properties of Rank Regressions (November 2007). Available at SSRN: https://ssrn.com/abstract=1028548 or http://dx.doi.org/10.2139/ssrn.1028548

Viktor Subbotin (Contact Author)

Department of Economics, Northwestern University ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

HOME PAGE: http://www.depot.northwestern.edu/ves418/indexjm.html

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