Locally R-optimal designs for a class of nonlinear multiple regression models

作     者：Lei He Rong-Xian Yue Lei He;Rong-Xian Yue

作者机构：Department of StistisAnhui Normal UniversityWuhuPeople's Republic of China Department of MathematisShanghai Normal UniversityShanghaiPeople's Republic of China 

出 版 物：《Statistical Theory and Related Fields》 (统计理论及其应用（英文）)

年 卷 期：2023年第7卷第2期

页      面：107-120页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 

基　　金：Lei He’s work is supported by the National Natural Science Foundation of China[Grant Number 12101013] the Natural Science Foundation of Anhui Province[Grant Number 2008085QA15] Rong-Xian Yue’s work is supported by the National Natural Science Foundation of China[Grant Numbers 11971318,11871143]. 

主　　题：Poisson regression models proportional hazards models R-optimality particle swarm optimization 

摘      要：This paper concerns with optimal designs for a wide class of nonlinear models with informa-tion driven by the linear predictor.The aim of this study is to generate an R-optimal design which minimizes the product of the main diagonal entries of the inverse of the Fisher informa tion matrix at certain values of the parameters.An equivalence theorem for the locally R optimal designs is provided in terms of the intensity function.Analytic solutions for the locally saturated R-optimal designs are derived for the models having linear predictors with and without intercept,respectively.The particle swarm optimization method has been employed to generate locally non-saturated R-optimal designs.Numerical examples are presented for ilustration of the locally R-optimal designs for Poisson regression models and proportional hazards regression models.