Unconditional limit theorems from conditional limit theorems

Mark Finkelstein and Howard G. Tucker

Journal of Nonparametric Statistics, 1997, vol. 8, issue 3, 267-274

Abstract: The method of proof developed here may be used to obtain unconditional limit theorems from conditional limit theorems in a variety of settings. It is known that given two samples with the same arbitrary nondegenerate common distribution function, the conditional distribution of the sum of the tied midranks of one sample within the pooled ordered sample, centered on its conditional expectation, and normed by the square root of its conditional variance, given the values of its numbers of ties, is asymptotically normal as the two sample sizes tend to infinity, provided that the proportions of ties obey a certain constraint. In this note the unconditional distribution of this same statistic is shown to be asymptotically normal also.

Date: 1997
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DOI: 10.1080/10485259708832724

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