Tie-break Bootstrap for Nonparametric Rank Statistics

In this paper, we propose a new bootstrap procedure for the empirical copula process. The procedure involves taking pseudo samples of normalized ranks in the same fashion as the classical bootstrap and applying small perturbations to break ties in the normalized ranks. Our procedure is a simple modification of the usual bootstrap based on sampling with replacement, yet it provides noticeable improvement in the finite sample performance. We also discuss how to incorporate our procedure into the time series framework. Since nonparametric rank statistics can be treated as functionals of the empirical copula, our proposal is useful in approximating the distribution of rank statistics in general. As an empirical illustration, we apply our bootstrap procedure to test the null hypotheses of positive quadrant dependence, tail monotonicity, and stochastic monotonicity, using U.S. Census data on spousal incomes in the past fifteen years.