| 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. |