The Bahadur Efficiency of the Power-Divergence Statistics Conditional on Margins for Testing homogeneity with Equal Sample Size

  • Kang, Seung-Ho (Department of Counseling, Educational Psychology and Special Education, Michigan State University, East Lansing, MI 48823, USA)
  • Published : 1997.12.01

Abstract

The family of power-divergence statistics conditional on margins is considered for testing homogeneity of .tau. multinomial populations with equal sample size and the exact Bahadur slope is obtained. It is shown that the likelihood ratio test conditional on margins is the most Bahadur efficient among the family of power-divergence statistics.

Keywords

References

  1. Some Limit Theorems in Statistics Bahadur, R. R.
  2. Proceedings of the third Berkeley Symposium and Mathematical Statistics and probability v.4 A statistical problem arising from retrospective studies Cornfield, J.
  3. Journal of the Royal Statistical Society Series B. v.46 Multinomial Goodness-of-Fit Tests Cressie, N.;Read, T. R. C.
  4. An Introduction to Probability Theory and Its Applications v.I Feller, W.
  5. Ph.D. dissertation, University of Wisconsin-Madison The conditional likelihood ratio test of independence in two-way contingency table Kang, S. H.
  6. The Annals of Statistics v.17 Bounds on the size of the Χ² test of independence in a contingency table Loh, W. Y,.
  7. Journal of Multivariate Analysis v.45 Bounds on the size of the likelihood ratio test of independence in a cotingency table Loh, W. Y.;Yu, X.
  8. Goodness-of-Fit Statistics for Discrete Multivariate Data Read, T. R. C.;Cressie, N.
  9. University of California Publication in Statistics v.2 Limit Theorems for Conditional Distributions Steck, G. P.