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October, 1971 The Asymptotic Behavior of the Smirnov Test Compared to Standard "Optimal Procedures"
George Kalish, Piotr W. Mikulski
Ann. Math. Statist. 42(5): 1742-1747 (October, 1971). DOI: 10.1214/aoms/1177693174


Let $X_1, X_2,\cdots, X_m, Y_1, Y_2,\cdots, Y_n$ be independent random samples from absolutely continuous distributions $F$ and $G$ respectively. Several standard tests of the hypothesis $H:F = G$ against the one-sided shift alternative $A: G(v) = F(v - \theta); (\theta > 0)$, are defined in terms of $F$. If, however, the true distributions of $X$'s and $Y$'s are $\Psi(v)$ and $\Psi(v - \theta)$ respectively, with $\Psi$ not necessarily equal to $F$, these tests are no longer optimal. It will be shown that there exist continuous distributions $\Psi$ (with density $\psi$), which are quite similar to $F$ but for which the Smirnov test--in terms of generalized Pitman efficiency (defined below) is considerably superior.


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George Kalish. Piotr W. Mikulski. "The Asymptotic Behavior of the Smirnov Test Compared to Standard "Optimal Procedures"." Ann. Math. Statist. 42 (5) 1742 - 1747, October, 1971.


Published: October, 1971
First available in Project Euclid: 27 April 2007

zbMATH: 0236.62034
MathSciNet: MR348910
Digital Object Identifier: 10.1214/aoms/1177693174

Rights: Copyright © 1971 Institute of Mathematical Statistics


Vol.42 • No. 5 • October, 1971
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