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.
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number
9030.
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Asparouhova, Elena & Golanski, Robert & Kasprzyk, Krzysztof & Sherman, Robert P. & Asparouhov, Tihomir, 2002.
"Rank Estimators For A Transformation Model,"
Econometric Theory,
Cambridge University Press, vol. 18(05), pages 1099-1120, July.
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