Copula模型的A-最优设计

A-optimal design of Copula model

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.