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Shangli Zhang,Zhide Fang,Hong Qin,Litao Han 한국통계학회 2011 Journal of the Korean Statistical Society Vol.40 No.2
In terms of the theory of inequality and the vectorization transformation of a matrix,we study the admissibility problem of linear estimators in growth curve models with inequality constraints. Under the quadratic loss and the matrix loss, we obtain the necessary and sufficient conditions for a linear estimator of estimable/inestimable linear functions being admissible in the homogeneous and inhomogeneous classes separately.
Construction of optimal designs for quantile regression model via particle swarm optimization
Zhai Yi,Xing Chen,Fang Zhide 한국통계학회 2023 Journal of the Korean Statistical Society Vol.52 No.4
As an extension of mean regression and being robust against outliers, quantile regression has been used in many fields such as biomedicine, ecology, economics. However, it is theoretically and computationally challenging to find the optimal experimental design for quantile regression due to the complexity of the optimiza- tion problem. The purpose of this paper is to provide theoretical necessary conditions for A- and c-optimality of a design separately, and a numerical algorithm to find optimal designs for quantile regression models. The algorithm is constructed through particle swarm optimization so as to solve the problem of non-convexity of optimality criteria. In this paper, the algorithm is applied to obtain locally as well as Bayesian optimal designs for Michaelis–Menten, Emax and Exponential quantile regression models. We demonstrate that this technique can be applied to a variety of optimality criteria and scale functions without making any further assumption.