R-optimality criterion for regression models with asymmetric errors

This paper is concerned with the problem of optimal designs for both linear and nonlinear regression models using the second-order least squares estimator when the error distribution is asymmetric. A new class of R-optimality criterion is proposed based on the second-order least squares estimator. An equivalence theorem for R-optimality is then established and used to check the optimality of designs. Moreover, several invariance properties of R-optimal designs are investigated. A few examples are presented for illustration and the relative efficiency comparisons between the second-order least squares estimator and the ordinary least squares estimator are discussed via the new criterion.