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Some invariance principles for mized rank statistics and induced order statistics and some application
Authors:Pranab Kumar Sen
Affiliation:Department of Biostatistics , University of North Carolina , Chapel Hill, N.C, 27514
Abstract:The structural affinity of mixed rank statistics and linear combinations of functions of concomitants of order statistics (or induced order statistics) is examined here. Some weal as well as strong invariance principles for these statistics are studied. A variety of models (depend on the nature of stochastic dependence of the two variates) is considered and the regularity conditions are tailored for these diverse situations. Some possible applications of these results in some problems of sequential (statistical) inference are also considered.
Keywords:concomitants of order statistics  contiguity  induced order statistics  invariance principles  martingals  mixed rank statistics  sequential tests  weak convergence  Wiener process
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