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July, 1975 On Functions of Order Statistics for Mixing Processes
K. L. Mehra, M. Sudhakara Rao
Ann. Statist. 3(4): 874-883 (July, 1975). DOI: 10.1214/aos/1176343188


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.


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K. L. Mehra. M. Sudhakara Rao. "On Functions of Order Statistics for Mixing Processes." Ann. Statist. 3 (4) 874 - 883, July, 1975.


Published: July, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0328.62031
MathSciNet: MR405544
Digital Object Identifier: 10.1214/aos/1176343188

Primary: 60F05
Secondary: 62G05 , 62G30

Keywords: empirical process , mixing processes , order statistics , quantile process , weak convergence

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 4 • July, 1975
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