Integral Expression Form of Admissible Linear Estimators of Effects in Linear Mixed Models

The problem of simultaneous linear estimation of fixed and random effects in the linear mixed model is considered. Necessary and sufficient conditions for a linear estimator of a linear function of fixed and random effects in balanced nested classification models to be admissible are given by Synowka(2008), and his admissible linear estimator is an integral expression. Wang(2009[10]) give another integral expression of this admissible linear estimator, and guesses that apart from these two integral expressions no longer have other integral expressions. Wang(2009[11]) get integral expressions of admissible linear estimators in balanced inverse nested classification models. A class of integral expressions of admissible linear estimators is given in the paper, besides Synowka's(2008) and Wang's(2009) results are special cases of these results.