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March, 1958 Testing the Hypothesis That Two Populations Differ Only in Location
Balkrishna V. Sukhatme
Ann. Math. Statist. 29(1): 60-78 (March, 1958). DOI: 10.1214/aoms/1177706706


Let $X_1, X_2, \cdots, X_n$ be $n$ independent identically distributed random variables with cumulative distribution function $F(x - \xi)$. Let $$\hat \xi(X_1, X_2, \cdots, X_n)$$ be an estimate of $\xi$ such that $\sqrt n(\hat \xi - \xi)$ is bounded in probability. The first part of this paper (Secs. 2 through 4) is concerned with the asymptotic behavior of $U$-statistics modified by centering the observations at $\hat \xi$. A set of necessary and sufficient conditions are given under which the modified $U$-statistics have the same asymptotic normal distribution as the original $U$-statistics. These results are extended to generalized $U$-statistics and to functions of several generalized $U$-statistics. The second part gives an application of the asymptotic theory developed earlier to the problem of testing the hypothesis that two populations differ only in location.


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Balkrishna V. Sukhatme. "Testing the Hypothesis That Two Populations Differ Only in Location." Ann. Math. Statist. 29 (1) 60 - 78, March, 1958.


Published: March, 1958
First available in Project Euclid: 27 April 2007

zbMATH: 0085.35405
MathSciNet: MR95559
Digital Object Identifier: 10.1214/aoms/1177706706

Rights: Copyright © 1958 Institute of Mathematical Statistics

Vol.29 • No. 1 • March, 1958
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