Abstract
Since Zellner (Bayesian and Non-Bayesian Estimation Using Balanced Loss Functions, pp. 377-390, 1994) proposed the balanced loss function, many researchers have been attracted to the field concerned. In this paper, under a generalized balanced loss function, we investigate the admissibility of linear estimators of the regression coefficient in general Gauss-Markov model (GGM) with respect to an inequality constraint. The necessary and sufficient conditions that the linear estimators of regression coefficient function are admissible are established, in the class of homogeneous/inhomogeneous linear estimation, respectively.MSC:62C05, 62F10.
Highlights
Throughout this paper, the symbols A, μ(A), A+, A, rk(A) and tr(A) stand for the transpose, the range, Moore-Penrose inverse, generalized inverse, rank, and trace of matrix A, respectively.Consider the following Gauss-Markov model:y = Xβ + ε, E(ε) =, Cov(ε) = σ In, ( . )where y is a n × observable random vector
Under a generalized balanced loss function, we investigate the admissibility of linear estimators of the regression coefficient in general Gauss-Markov model (GGM) with respect to an inequality constraint
In this paper, considering model ( . ) with the balanced loss ( . ), we investigate the admissibility of linear estimator of regression coefficient in the linear model with an inequality constraint
Summary
Throughout this paper, the symbols A , μ(A), A+, A–, rk(A) and tr(A) stand for the transpose, the range, Moore-Penrose inverse, generalized inverse, rank, and trace of matrix A, respectively. The balanced loss function takes both the precision of the estimator and the goodness-of-fit of the model into account. For the linear model with an inequality constraint, [ – ] studied the admissibility of linear estimator of parameters in the univariate and multivariate linear models under the quadratic and matrix loss, respectively. R A Y , β, σ = σ w tr VD+ – w tr A VD+X + tr A VA B + β (A X – Ip) B(A X – Ip)β = σ w tr VD+ – w tr AVD+X + tr AVA B + β (AX – Ip) B(AX – Ip)β = R AY , β, σ It implies that no estimator is better than AY. It means there does not exist an estimator that is better than AY + a.
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