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- W2034133761 abstract "In this paper linear restrictions on regression coefficients are studied. Let the $p times q_2$ matrix of coefficients of regression of the $p$ dependent variates on $q_2$ of the independent variates be $mathbf{bar B}_2$. Maximum likelihood estimates of an $m times p$ matrix $Gamma$ satisfying $Gamma'mathbf{bar B}_2 = 0$ and certain other conditions are found under the assumption that the rank of $mathbf{bar B}_2$ is $p - m$ and the dependent variates are normally distributed (Section 2). Confidence regions for $Gamma$ under various conditions are obtained (Section 5). The likelihood ratio test of the hypothesis that the rank of $mathbf{bar B}_2$ is a given number is obtained (Section 3). A test of the hypothesis that $Gamma$ is a certain matrix is given (Section 4). These results are applied to the $q$-sample problem (Section 7) and are extended for certain econometric models (Section 6)." @default.
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- W2034133761 date "1951-09-01" @default.
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- W2034133761 title "Estimating Linear Restrictions on Regression Coefficients for Multivariate Normal Distributions" @default.
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- W2034133761 doi "https://doi.org/10.1214/aoms/1177729580" @default.
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