Abstract
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.
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