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January, 1980 On Efficiency and Optimality of Quadratic Tests
Gavin G. Gregory
Ann. Statist. 8(1): 116-131 (January, 1980). DOI: 10.1214/aos/1176344895

Abstract

Let $Z_1, Z_2, \cdots$ be i.i.d. standard normal variables. Results are obtained which relate to the tail behavior as $x \rightarrow \infty$ of distributions of the form $F(x) = P\{\sum^\infty_{k=1}\lambda_k\lbrack(Z_k + a_k)^2 - 1\rbrack \leqslant x\}$. For test statistics which have such limiting distributions $F$, asymptotic relative efficiency measures are discussed. One of these is the limiting approximate Bahadur efficiency. Applications are to tests of fit and tests of symmetry.

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Gavin G. Gregory. "On Efficiency and Optimality of Quadratic Tests." Ann. Statist. 8 (1) 116 - 131, January, 1980. https://doi.org/10.1214/aos/1176344895

Information

Published: January, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0424.62012
MathSciNet: MR557558
Digital Object Identifier: 10.1214/aos/1176344895

Subjects:
Primary: 62E15
Secondary: 62E20 , 62G10

Keywords: $U$-statistic , Bahadur efficiency , Chi-square test , Cramer-von Mises test

Rights: Copyright © 1980 Institute of Mathematical Statistics

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Vol.8 • No. 1 • January, 1980
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