MULTIVARIATE REGRESSION WITH ONE STOCHASTIC PREDICTOR VARIABLE.
STANFORD UNIV CALIF DEPT OF STATISTICS
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Estimators are obtained which dominate the maximum likelihood estimator for the parameters in the regression of at least three dependent variables on one stochastic independent variable, these variables being jointly normally distributed. The loss function corresponds to that for the following problem given a random sample of N observations from the joint normal distribution of all the variables and an additional independent observation on the independent variable, to predict the corresponding value of the dependent variables, when the loss function is the conditional mean square of the distance between the predicted and the actual values in the metric of the residual covariance matrix, given the sample of N observations. It is proved that the maximum likelihood estimator is admissible when there are only two dependent variables and the means of the dependent variables and independent variable are known. Author
- Statistics and Probability