论文信息 - Locally Best Invariant Test for Sphericity and the Limiting Distributions

Locally Best Invariant Test for Sphericity and the Limiting Distributions

The locally best invariant test for testing sphericity in a multivariate normal distribution is obtained. It is different from the likelihood ratio criterion. Some other known results are remarked. The limiting distributions of the test statistics are investigated. In particular Pitman efficiency of the likelihood ratio test with respect to the locally best invariant test is shown to be one for normal alternatives.

N. Sugiura

[1] A. James. The Distribution of the Latent Roots of the Covariance Matrix , 1960 .

[2] A. Constantine. Some Non-Central Distribution Problems in Multivariate Analysis , 1963 .

[3] A. James. Distributions of Matrix Variates and Latent Roots Derived from Normal Samples , 1964 .

[4] Richard Schwartz,et al. Locally Minimax Tests , 1967 .

[5] N. Giri,et al. On Tests of the Equality of Two Covariance Matrices , 1968 .

[6] N. Sugiura,et al. Asymptotic Expansions of the Distributions of the Likelihood Ratio Criteria for Covariance Matrix , 1969 .

[7] K. Pillai,et al. On the Distributions of the Ratios of the Roots of a Covariance Matrix and Wilks' Criterion for Tests of Three Hypotheses , 1969 .

[8] H. Nagao,et al. Asymptotic expansions of some test criteria for homogeneity of variances and covariance matrices from normal populations , 1970 .

[9] Y. Fujikoshi. Asymptotic expansions of the distributions of test statistics in multivariate analysis , 1970 .

[10] S. John. Some optimal multivariate tests , 1971 .