论文信息 - The likelihood ratio tests for the dimensionality of regression coefficients

The likelihood ratio tests for the dimensionality of regression coefficients

In this paper we give a unified derivation of the likelihood ratio (LR) statistics for testing the hypothesis on the dimensionality of regression coefficients under a usual MANOVA model. We also derive the LR statistics under a general MANOVA model and study their asymptotic null and nonnull distributions. Further it is shown that the test statistic used by Bartlett [4] for testing the hypothesis that the last p-k canonical correlations are all zero is the LR statistic.

Yasunori Fujikoshi | Y. Fujikoshi

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

[2] P. Hsu,et al. On the Limiting Distribution of Roots of a Determinantal Equation , 1941 .

[3] T. W. Anderson. Estimating Linear Restrictions on Regression Coefficients for Multivariate Normal Distributions , 1951 .

[4] Calyampudi R. Rao,et al. The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves. , 1965, Biometrika.

[5] T. W. Anderson. The Asymptotic Distributions of the Roots of Certain Determinantal Equations , 1948 .

[6] Y. Fujikoshi. Monotonicity of the Power Functions of Some Tests in General Manova Models , 1973 .

[7] C. G. Khatri,et al. A note on a manova model applied to problems in growth curve , 1966 .

[8] R. Potthoff,et al. A generalized multivariate analysis of variance model useful especially for growth curve problems , 1964 .

[9] Yasunori Fujikoshi,et al. Asymptotic expansions of the non-null distributions of three statistics in GMANOVA , 1974 .

[10] P. Hsu,et al. ON THE LIMITING DISTRIBUTION OF THE CANONICAL CORRELATIONS , 1941 .