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2005•Chinese Journal of Applied Probability and StatistiesRequires access

Posterior Likelihood Ratio Tests for Multivariate Linear Model Based On Normal-Inverse Wishart Prior

G Hang

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Abstract

The problem of linear hypothesis testing of the multivariate normal linear model Y - Nn×m (XB, In (?) ∑) is considered under the normal-inverse Wishart prior distribution of the parameter matrices (B,∑@). Two posterior likelihood ratio tests for the linear hypothesis about the parameter matrix B are constructed. The likelihood ratio statistics obtained from the posterior distribution of B are functions of the characteristic roots of the random matrices which have matric F-distribution.

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What this paper is about

The problem of linear hypothesis testing of the multivariate normal linear model Y - Nn×m (XB, In (?) ∑) is considered under the normal-inverse Wishart prior distribution of the parameter matrices (B,∑@). Two posterior likelihood ratio tests for the linear hypothesis about the parameter matrix B are constructed. The likelihood ratio statistics obtained from the posterior distribution of B are functions of the characteristic roots of the random matrices which have matric F-distribution.

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Available abstract

The problem of linear hypothesis testing of the multivariate normal linear model Y - Nn×m (XB, In (?) ∑) is considered under the normal-inverse Wishart prior distribution of the parameter matrices (B,∑@). Two posterior likelihood ratio tests for the linear hypothesis about the parameter matrix B are constructed. The likelihood ratio statistics obtained from the posterior distribution of B are functions of the characteristic roots of the random matrices which have matric F-distribution.

Key concepts: Wishart distribution, Inverse-Wishart distribution, Mathematics, Matrix t-distribution, Normal-Wishart distribution, Matrix normal distribution, Statistics, Likelihood-ratio test

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