Copula模型的A-最优设计  

A-optimal design of Copula model

作　　者：孟玉莹 刘欣[1] MENG Yuying;LIU Xin(College of Science,Donghua University,Shanghai,China)

机构地区：[1]东华大学理学院,上海

出　　处：《东华大学学报（自然科学版）》2024年第5期181-186,共6页Journal of Donghua University(Natural Science)

基　　金：国家自然科学基金(11871143);上海市自然科学基金(24ZR1401500)。

摘　　要：Copula模型广泛应用于经济与金融等领域,研究其最优设计问题可给出更具统计推断效力的试验方案。研究Copula模型的A-最优设计问题,利用方向导数建立二元Copula模型的A-最优设计的等价性定理,为A-最优设计的求解和验证提供理论工具。基于这一工具获得了边际模型为一次回归的Gaussian Copula模型和边际模型为logistic回归的Product Copula和Clayton Copula模型的A-最优设计,说明了等价性定理的作用。The Copula model is widely used in fields such as economics and finance,and studying its optimal design problem can provide experimental plans with more statistical inference power.This paper studies the A-optimal design problem of the Copula model and establishes an equivalence theorem for the A-optimal design of the bivariate Copula model using directional derivatives,providing a theoretical tool for solving and verifying the A-optimal design.Based on this tool,the A-optimal designs of the Gaussian Copula model with a linear regression marginal model and the Product Copula and Clayton Copula models with a logistic regression marginal model were obtained,demonstrating the effectiveness of the equivalence theorem.

关 键 词：COPULA模型 A-最优设计 等价性定理 灵敏度函数 

分 类 号：O212.6[理学—概率论与数理统计]