Open Access
March, 1977 On a Conjecture About the Limiting Minimal Efficiency of Sequential Tests
Sture Holm
Ann. Statist. 5(2): 375-378 (March, 1977). DOI: 10.1214/aos/1176343802


For use in comparisons of sequential and nonsequential tests Berk (Ann. Statist. 3 991-998) has defined the limiting relative efficiency of sequential tests as the limiting ratio of the expected sample size under the null hypothesis and the supremum over the parameter set of the expected sample size. He has proved that for the symmetric binomial case the limiting relative efficiency of a class of SPR type tests coincides with a related quantity for SPR tests of drift in a Wiener process. He has also conjectured that this result applies to a more general class. In this note we prove that it holds for exponential families satisfying some mild regularity conditions.


Download Citation

Sture Holm. "On a Conjecture About the Limiting Minimal Efficiency of Sequential Tests." Ann. Statist. 5 (2) 375 - 378, March, 1977.


Published: March, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0368.62059
MathSciNet: MR445742
Digital Object Identifier: 10.1214/aos/1176343802

Primary: 62L10
Secondary: 60G40 , 62E20 , 62F20

Keywords: 62F5 , limiting minimal efficiency , sequential analysis , sequential test

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 2 • March, 1977
Back to Top