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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.

Admissibility in general linear model with respect to an inequality constraint under balanced loss