Application of the Skorokhod Representation Theorem to Rates of Convergence for Linear Combinations of Order Statistics

Abstract

Rates of convergence for linear combinations of order statistics are obtained. The work is in the spirit of those authors who have used in one form or another the weak convergence of the sample empirical process to a tied-down Wiener process, except that the Skorokhod embedding is explicitly used to obtain a rate of convergence via control on the tail-behavior of the stopping times. The paper concludes with a remark on the limitations of the technique as far as getting the best possible rate is concerned.