On Functions of Order Statistics for Mixing Processes

Abstract

Recent results of Shorack (Ann. Math. Statist. (1972) 412-427) on the asymptotic normality of functions of order statistics are extended to stationary $\phi$-mixing processes and to a class of strong mixing processes. The results of this paper are based on the weak convergence of empirical processes relative to the metric $d_q$ as developed in Fears and Mehra (Ann. Statist. (1974) 586-596). Some remarks on trimmed and Winsorized means in the strong mixing case are also included.