Estimation and Tests for Unknown Linear Restriction in Multivariate Linear Models.
PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS
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This report considers the multivariate linear regression model X F1 Xi F2 E, where X is a c x N matrix of observations, F1 is a known c x p matrix of covariates, F2 is a known m x N design matrix containing values of independent variables in the regression, and XI is an unknown p x m matrix of regression coefficients assumed under a null hypothesis H0 to satisfy a system of linear restraints of the form H0 U1 Xi F3 ab, where F3 m x k and b s x h are known matrices, and U1 r x p and alpha r x s s or r or p are unknown matrices of restraint coefficients. The error matrix E c x N is assumed to have columns which are statistically independent, multivariate normal random vectors with common mean vector 0 and common unknown matrix sigma.
- Statistics and Probability