Abstract
The definitions of $\Phi$ optimality and $\Phi$ admissibility of stochastic regression coefficients are given in a general multivariate random effects model under the generalized balanced loss function. $\Phi$ admissibility of linear estimators of stochastic regression coefficients is investigated. Sufficient and necessary conditions for linear estimators to be $\Phi$ admissible in classes of homogeneous and nonhomogeneous linear estimators are obtained, respectively.
Highlights
It assumes here that Σ12 is zero matrix, which means that stochastic regression coefficient B is uncorrelated with random error e
−1 1 c0 where 0.75 < c < 1, we can still verify that LY is Φ admissible in a class of homogeneous linear estimators
We investigate Φ admissible estimators of stochastic regression coefficients in a multivariate random effects model with respect to generalized balanced loss function
Summary
The corresponding result can be obtained by matrix calculations according to Theorem 2.1, which is given as follows. Under model (1.1) and loss function (1.2) where q = 1, LY L∼H B if and only if (a), (b), (c) and (d) in Theorem 2.1 hold simultaneously. Under the conditions of Corollary 2.6, if it further assumes that K = I, Σ11 = 0, Σ22 ≥ 0 and K = I, Σ11 = 0, Σ22 > 0 respectively, it can get the main results of [10] and [28] from Theorem 2.1, which we omit here.
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