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.
"On Functions of Order Statistics for Mixing Processes." Ann. Statist. 3 (4) 874 - 883, July, 1975. https://doi.org/10.1214/aos/1176343188