A Normal Approximation for the Multivariate Likelihood Ratio Statistics
For many multivariate hypotheses, under the normality assumptions, the likelihood ratio tests are optimal in the sense of having maximal exact slopes. The exact distributions needed for implementing these tests are complex and their tabulation is limited in scope and accessibility. In this paper, a method of constructing normal approximations to these distributions is described, and illustrated using the problems of testing sphericity and independence between two sets of variates. The normal approximations are compared with well-known competing approximations and are seen to fare well.
Key WordsSphericity independence between two sets of variates
Unable to display preview. Download preview PDF.
- Bahadur, R.R. (1967). An optimal property of the likelihood ratio statistics. Proceedings of Fifth Berkeley Symposium Mathematical Statistics and Probability. University of California Press. Pages 13–26.Google Scholar
- Engelman, L., Frane, J.W., Jennrich, R.I. (1977). Biomedical Computer Programs P-Series. University of California Press, Berkeley, California.Google Scholar
- Krishnaiah, P.R. (1979). Some Recent Developments on The Real Multivariate Distributions. North Holland Co., New York.Google Scholar
- Nayer, P.P.N. (1936). An investigation into the application of Neyman and Pearson’s L1 test, with tables of percentage limits. Statistical Research Memorandum, 1, 38. University of London.Google Scholar
- Neyman, J., Pearson, E.S. (1931). On the problem of k samples. Bulletin International Academy Cracovie, A, 6, 460.Google Scholar