Multiple Parameter Estimation In The Linear Model May Allow,

Admissibility is one of the important criterions to compare the goodness of estimations in the view of statistical decision. In linear model, admissibility of linear models with constraints under quadratic loss functionL₂ (D(Y), SXB) = (D(Y) - SXB)'C_t (D(Y) - SXB) and matrix loss functionL₁(D(Y), SXB) = (D(Y)-SXB)C_m(D(Y)-SXB)are usually investigated. The theorem about the admissibility with the known covariance is comparative maturity, and includes integrated systemic results. In some widely applicable models, the paper studies the admissibility of parameter linear estimators and gets some sufficient and necessary conditions with unknown covariance. We enrich the content of admissibility theory.Firstly, we state some basic information about matrix and admissibility. Secondly, we study the admissibility of the linear model with unknown covariance, and also get some sufficient and necessary conditions when the underlying distribution is a normal one with unknown covariance. In view of practical situation, regression parameters of linear regression usually don't vary in Euclidean space and they may be restricted with some conditions. We can known the value of them more or less because of property of trial or prior information based on objective meaning of parameter. For example, component nonnegative, the sum of component is zero and so on. So we often confront with restricted situation. Lastly, we study the linear model with incomplete ellipsoidal restricted condition and get some results of admissibility of estimator.