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The Invariance Principle for One-Sample Rank-Order Statistics
Pranab Kumar Sen
The Annals of Statistics
Vol. 2, No. 1 (Jan., 1974), pp. 49-62
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2958380
Page Count: 14
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Analogous to the Donsker theorem on partial cumulative sums of independent random variables, for a broad class of one-sample rank order statistics, weak convergence to Brownian motion processes is studied here. A simple proof of the asymptotic normality of these statistics for random sample sizes is also presented. Some asymptotic results on renewal theory for one-sample rank order statistics are derived.
The Annals of Statistics © 1974 Institute of Mathematical Statistics