二阶最小二乘估计下多因子非线性模型的贝叶斯Ψ_(q)-最优设计

Bayesian Ψ_(q)-Optimal Designs for Multi-Factor Nonlinear Models Based on the Second-Order Least Squares Estimator

许多研究表明,回归模型的误差为非对称分布时,二阶最小二乘估计比普通最小二乘估计更有效.文章基于参数的二阶最小二乘估计方法研究了多因子非线性模型的贝叶斯Ψ_(q)-最优设计.文章证明了当模型中含有常数项时,该模型的贝叶斯Ψ_(q)-最优设计等同于普通最小二乘估计下的贝叶斯Ψ_(q)-最优设计;当模型中不含常数项时,如果边际模型的贝叶斯Ψ_(q)-最优设计满足正交假设条件,则多因子非线性模型的贝叶斯Ψ_(q)-最优设计为边际模型最优设计的乘积设计.最后,文章通过几个例子验证了理论结果的有效性.

As the error in a regression model obeys an asymmetric distribution,it has been shown that the second-order least squares estimator is more efficient than the ordinary least squares estimator.This paper considers Bayesian Ψ_(q)-optimal designs for multi-factor nonlinear models under the second-order least squares estimation.For such a multi-factor nonlinear model with a constant term,its Bayesian Ψ_(q)-optimal design via the second-order least squares estimator is the same as that derived from the ordinary least squares estimator.For the multi-factor nonlinear model without a constant term,if orthogonal assumptions are satisfied for Bayesian Ψ_(q)-optimal designs on marginal models,then Bayesian Ψ_(q)-optimal design for multi-factor nonlinear model can be obtained from the product design of Bayesian Ψ_(q)-optimal designs on marginal models.Several examples are presented to illustrate the effectiveness of theoretical results.