Rates of convergence for linear rank statistics with dependent data

Abstract

Asymptotic distributions and rates of convergence are obtained for linear rank statistics with dependent random variables. It is assumed that the dependent random variables can be written as a set of N independent random vectors. The lengths of the independent random vectors are allowed to be unequal, but bounded; and the distribution functions of the vectors are arbitrary. Some results are given for certain unbounded score functions with approximate scores; most results assume that the score function has a bounded second derivative. The results are especially suitable for deriving asymptotic rank tests for models with dependent observations and unequal cell sizes, such as stratified random effects models and repeated measures designs with missing observations.