Some Convergence Theorems for Ranks and Weighted Empirical Cumulatives
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.
Permanent link to this document: http://projecteuclid.org/euclid.aoms/1177696824
Digital Object Identifier: doi:10.1214/aoms/1177696824
Mathematical Reviews number (MathSciNet): MR267631
Zentralblatt MATH identifier: 0232.62020