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October, 1970 Some Convergence Theorems for Ranks and Weighted Empirical Cumulatives
Hira Lal Koul
Ann. Math. Statist. 41(5): 1768-1773 (October, 1970). DOI: 10.1214/aoms/1177696824


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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Hira Lal Koul. "Some Convergence Theorems for Ranks and Weighted Empirical Cumulatives." Ann. Math. Statist. 41 (5) 1768 - 1773, October, 1970.


Published: October, 1970
First available in Project Euclid: 27 April 2007

zbMATH: 0232.62020
MathSciNet: MR267631
Digital Object Identifier: 10.1214/aoms/1177696824

Rights: Copyright © 1970 Institute of Mathematical Statistics

Vol.41 • No. 5 • October, 1970
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