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September, 1976 Power Bounds for a Smirnov Statistic in Testing the Hypothesis of Symmetry
Hira Lal Koul, R. G. Staudte Jr.
Ann. Statist. 4(5): 924-935 (September, 1976). DOI: 10.1214/aos/1176343589

Abstract

Lower and upper bounds on the power of a Smirnov test for symmetry $H_0: \bar{F} = F$ versus $H_1: \bar{F} \geqq F, \sup_x\lbrack\bar{F}(x) - F(x)\rbrack = \Delta > 0$ are obtained exactly or estimated for selected values of sample size $N$, level $\alpha$, and asymmetry $\Delta$. Furthermore the asymptotic power of the test as $N^{\frac{1}{2}}\Delta_N \rightarrow c$ is shown to be bounded by $\Phi(c - k_\alpha)$ and 1 if $c \geqq k_\alpha$ and by $\alpha$ and $2\Phi(c - k_\alpha)$ if $c < k_\alpha$, where $k_\alpha$ is the critical point. These bounds compare favorably in some respects with those of the Wilcoxon and other monotone rank tests studied in "Power bounds and asymptotic minimax results for one-sample rank tests," Ann. Math. Statist. 42 12-35.

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Hira Lal Koul. R. G. Staudte Jr.. "Power Bounds for a Smirnov Statistic in Testing the Hypothesis of Symmetry." Ann. Statist. 4 (5) 924 - 935, September, 1976. https://doi.org/10.1214/aos/1176343589

Information

Published: September, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0339.62023
MathSciNet: MR471170
Digital Object Identifier: 10.1214/aos/1176343589

Subjects:
Primary: 62G10

Keywords: monotone rank tests , power bounds , Smirnov statistics

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 5 • September, 1976
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