Simultaneous tests for equality of latent roots against certain alternatives-II

Abstract : The authors proposed a procedure for testing for the equality of latent roots of a matrix, when the associated random matrix has certain distribution, against the alternative that at least two of the roots are unequal. The random matrices considered are (1) Wishart matrix; (2) (S sub 1)(S sub 2)superscript -1; (3) matrix connected with MANOVA; and, (4) matrix associated with canonical correlations; here S sub 1 and S sub 2 are independently distributed central Wishart matrices. (Author)

[1]  T. W. Anderson.  ASYMPTOTIC THEORY FOR PRINCIPAL COMPONENT ANALYSIS , 1963 .

[2]  T. Sugiyama.  On the Distribution of the Largest Latent Root of the Covariance Matrix , 1967 .

[3]  M. A. Girshick.  The Distribution of the Ellipticity Statistic Le when the Hypothesis is False , 1941 .

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

[5]  A. James.  The Distribution of Noncentral Means with Known Covariance , 1961 .

[6]  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 .

[7]  T. Sugiyama,et al.  Joint Distribution of the Extreme Roots of a Covariance Matrix , 1970 .

[8]  C. G. Khatri,et al.  On the Non-Central Distributions of Two Test Criteria in Multivariate Analysis of Variance , 1968 .

[9]  George A. Anderson,et al.  An Asymptotic Expansion for the Distribution of the Latent Roots of the Estimated Covariance Matrix , 1965 .

[10]  C. G. Khatri,et al.  Some Distribution Problems Connected with the Characteristic Roots of $S_1S^{-1}_2$ , 1967 .

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

[12]  Mituaki Huzii.  Note on the estimation of correlogram by using transformed variables , 1971 .

[13]  S. Kullback,et al.  Some Aspects of Multivariate Analysis. , 1958 .

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