Some Convergence Theorems for Ranks and Weighted Empirical Cumulatives
The Annals of Mathematical StatisticsPublished 1 October 1970Open access
Hira L. Koul
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Abstract
In this paper two convergence theorems are proved. One gives a strong law of large numbers for a class of linear rank statistics and the other gives weak convergence of a weighted empirical cumulative process to Gaussian process, concentrated on continuous sample functions. Of course, both of these results are true under some regularity condition on the quantities involved.
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Computer ScienceMathematics