OPTIMUM DESIGN ACCOUNTING FOR THE GLOBAL NONLINEAR BEHAVIOR OF THE MODEL

• 成果类型: Article
• 署名作者: Pazman, Andrej; Pronzato, Luc
• 署名单位: Comenius University Bratislava; Centre National de la Recherche Scientifique (CNRS); Universite Cote d'Azur
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/14-AOS1232
• 发表日期: 2014
• 页码: 1426-1451
• 关键词: regression

摘要

Among the major difficulties that one may encounter when estimating parameters in a nonlinear regression model are the nonuniqueness of the estimator, its instability with respect to small perturbations of the observations and the presence of local optimizers of the estimation criterion. We show that these estimability issues can be taken into account at the design stage, through the definition of suitable design criteria. Extensions of E-, c- and G-optimality criteria are considered, which when evaluated at a given theta(0) (local optimal design), account for the behavior of the model response eta(theta) for theta far from theta(0). In particular, they ensure some protection against close-to-overlapping situations where parallel to eta(theta) - eta(theta(0))parallel to is small for some theta far from theta(0). These extended criteria are concave and necessary and sufficient conditions for optimality (equivalence theorems) can be formulated. They are not differentiable, but when the design space is finite and the set Theta of admissible theta is discretized, optimal design forms a linear programming problem which can be solved directly or via relaxation when Theta is just compact. Several examples are presented.