Admissibility Of Parameter Estimators In Linear Model Under Vector Loss Function

Admissibility is one of the important criterions to compare the goodness of estimators in the view of statistical decision. In linear model, the theorem about the admissibility under the quadric loss function or under the matrix loss function is comparative maturity, and includes integrated systemic results [2]-[4]. The study about the admissibility of parameter estimators in linear model under vector loss function becomes one of the new subjects of studying about admissibility since Zhao Jianxin put forward the vector loss function in 1999. In some widely applicable models, the paper studies the admissibility of parameter linear estimators and gets some sufficient and necessary conditions or some sufficient conditions about admissibility of parameter estimators. We enrich the content of admissibility theory.At first, when the random error matrix is known and positive definite, we discuss the admissibility of parameter estimator in simple linear model . On the base, using the knowledge about matrix operations, we study the admissibility of parameter estimators in multilinear model and growth curve model. We get some sufficient and necessary conditions or some sufficient conditions about the admissibility of parameter estimators among the special estimator classes or the general class.And then, when the random error matrix is unknown, this paper discusses the admissibility of linear estimators of the mean parameter in the (H) model and gets several necessary and sufficient conditions about the admissibility of parameter estimators.