Near-exact and new asymptotic distributions for some Bahadur-optimal likelihood ratio test statistics in multivariate normal populations
by
Carlos Coelho
Department of Mathematics, Instituto Sup. de Agronomia, 1349-017 Lisboa, PORTUGAL
Coauthors: Ashis SenGupta (Applied Statistics Unit, Indian Statistical Institute,203 Barrackpore Trunk Road,Calcutta 700035, India), R.P. Albreto (Department of Mathematics, Instituto Sup. de Agronomia, 1349-017 Lisboa, PORTUGAL)

An important class of testing problems with multivariate normal populations consists of the following:

i) the general linear hypothesis, ii) the equality of q covariance matrices, iii) the equality of q independent distributions, iv) the independence of m sets of variables and v) the sphericity of a covariance matrix. Also, likelihood ratio test statistics or their simple modifications corresponding to all the above problems are known to yield Bahadur-optimal tests. Near-exact and asymptotic distributions that match the two or three first exact moments are considered for these likelihood ratio test statistics. Both numerical and analytical results on the quality of the approximations are given. Evidence is obtained that the near-exact and asymptotic distributions presented behave much better than the known asymptotic distributions.

Date received: October 16, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafr-60.