Open Access
May, 1976 Tests for Independence in Infinite Contingency Tables
Shingo Shirahata
Ann. Statist. 4(3): 542-553 (May, 1976). DOI: 10.1214/aos/1176343460


This paper deals with distribution-free tests for independence under the constraint that the population has a bivariate discrete distribution. The locally most powerful conditional test, given the marginal empirical distributions, is derived. The unconditional asymptotic distribution of the conditional test statistic standardized by the conditional mean and variance is also given under the hypothesis of independence and under contiguous alternatives. Furthermore, some discussions on asymptotic relative efficiency are made. Two competitive test statistics having asymptotically chi-square distributions with different degrees of freedom are compared by means of the local asymptotic relative efficiency.


Download Citation

Shingo Shirahata. "Tests for Independence in Infinite Contingency Tables." Ann. Statist. 4 (3) 542 - 553, May, 1976.


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

zbMATH: 0337.62029
MathSciNet: MR405710
Digital Object Identifier: 10.1214/aos/1176343460

Primary: 62G10
Secondary: 62E20 , 62G20

Keywords: asymptotic normality , conditional test , Contingency table , discrete distribution , Distribution-free test for independence , local asymptotic relative efficiency , rank test

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 3 • May, 1976
Back to Top