Open Access
Translator Disclaimer
January, 1973 The Most Powerful Scale and Location Invariant Test of the Normal Versus the Double Exponential
Vincent A. Uthoff
Ann. Statist. 1(1): 170-174 (January, 1973). DOI: 10.1214/aos/1193342395

Abstract

The most powerful scale and location invariant test of normality against the double exponential alternative is derived by the technique of integrating with respect to the scale and location transformation group. The resultant test is asymptotically equivalent to the likelihood ratio test of this hypothesis and to Geary's test (i.e. mean deviation over standard deviation) for all three test statistics are shown to have the same asymptotic normal distribution when the sampling is from a symmetric, absolutely continuous distribution, whose density is continuous in the neighborhood of its median and whose fourth moment exists.

Citation

Download Citation

Vincent A. Uthoff. "The Most Powerful Scale and Location Invariant Test of the Normal Versus the Double Exponential." Ann. Statist. 1 (1) 170 - 174, January, 1973. https://doi.org/10.1214/aos/1193342395

Information

Published: January, 1973
First available in Project Euclid: 25 October 2007

zbMATH: 0255.62026
MathSciNet: MR381093
Digital Object Identifier: 10.1214/aos/1193342395

Subjects:
Primary: 62F05
Secondary: 62A05

Rights: Copyright © 1973 Institute of Mathematical Statistics

JOURNAL ARTICLE
5 PAGES


SHARE
Vol.1 • No. 1 • January, 1973
Back to Top