Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models |
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Authors: | Qiguang Wu and Guoqing Yang |
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Institution: | Institute of Systems Science, Academy of Mathematics and System Sciences, Chinese Academy of Sciences,Beijing 100080, China |
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Abstract: | In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class
of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve
model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given
for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively.
Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature
for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions
for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there
exist UMRE estimators of parameters in the variance components model are obtained for the first time. |
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Keywords: | uniformly minimum risk equivariant estimator affine group of transformations quadratic loss matrix loss |
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