Abstract
LetY have ann-variate normal distribution with covariance matrixσ 2I and mean vectorXβ, whereX is a knownn×p matrix. The problem of estimatingθ=σ 2+β′X′CXβ is studied. The admissibility and inadmissibility of the estimators of the form\(b\hat S^2 + \hat \beta 'X'CX\hat \beta \), where\(\hat \beta = (X'X)^ - X'Y\) and\(S^2 = (Y - X\hat \beta )'(Y - X\hat \beta )\), are established. Another class of admissible quadratic estimators ofθ is derived.
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This work is supported by the National Natural Science Foundation of China.
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Wu, Q. Quadratic estimators of quadratic functions with parameters in normal linear models. Acta Mathematicae Applicatae Sinica 11, 378–388 (1995). https://doi.org/10.1007/BF02007176
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DOI: https://doi.org/10.1007/BF02007176