Assume that a real linear model y = X beta + epsilon is over-parameterized as y = X beta + Z gamma + epsilon by adding some new regressors Z gamma. In such a case, results of statistical inferences of the unknown para...
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Assume that a real linear model y = X beta + epsilon is over-parameterized as y = X beta + Z gamma + epsilon by adding some new regressors Z gamma. In such a case, results of statistical inferences of the unknown parameters beta and epsilon under the two models are not necessarily the same. This paper aims at characterizing relationships between the best linear unbiased predictors (BLUPs) of the joint vector phi = K beta + J epsilon of the unknown parameters in the two models. In particular, we derive necessary and sufficient conditions for the BLUPs of phi to be equivalent under the real model and its over-parameterized counterpart.
Assume that a true multivariate general linear model for an observed random matrix is over-parameterized by adding some new regressors due to model uncertainty. Then predictors and estimators of parameter spaces in th...
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Assume that a true multivariate general linear model for an observed random matrix is over-parameterized by adding some new regressors due to model uncertainty. Then predictors and estimators of parameter spaces in the true and over-parameterized models are not necessarily the same. In this article, we study the comparison problem of predictors/estimators of parameter spaces under the two models. In particular, we derive necessary and sufficient conditions for the best linear unbiased predictors/best linear unbiased estimators of the parameter spaces to be equivalent under the two models. (C) 2017 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.
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