Open Access
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

Abstract

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.

Citation

Download Citation

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

Information

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
Back to Top