Construction of optimal designs for quantile regression model via particle swarm optimization

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Journal of the Korean Statistical Society


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 optimization 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.