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On Limiting Distributions of Intermediate Order Statistics from Stationary Sequences.
NORTH CAROLINA UNIV AT CHAPEL HILL INST OF STATISTICS
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The problem of finding the asymptotic distribution of the maximum term from a stationary dependent sequence of random variables r.v.s has been extensively investigated in the literature. Of particular interest are the cases in which the concept of approximate independence is formulated mathematically in terms of conditions such as strong mixing or, for normal sequences, conditions on the rate of decay of the covariances. Our objective in this paper is to obtain analogous results for so-called intermediate order statistics. A sequence is given of intermediate order statistics and intermediate rank sequence. These conditions parallel those used to obtain the corresponding result in the extreme order statistic problem, a primary difference being that certain more rapid mixing rates have to be assumed. Using our procedure it is convenient to deal directly with an appropriate level exceedance problem and to regard that of asymptotic distributions as a specialization.
APPROVED FOR PUBLIC RELEASE