论文标题
设计以检测回归模型中的异质性
Designing to detect heteroscedasticity in a regression model
论文作者
论文摘要
我们考虑设计实验的问题，以检测非线性高斯回归模型中指定的异质体性的存在。在此框架中，我们专注于$ {\ rm d} _s $ - 和kl-criteria，并研究了它们与基于可能性测试的渐近性卡方分布的非中心性参数的关系，用于本地替代方案。具体而言，我们发现，当方差函数仅取决于一个参数时，这两个标准渐近地重合，尤其是$ {\ rm d} _1 $ - criterion与非中心参数成正比。以不同的方式，如果方差函数取决于参数的向量，则KL-Optimum Design会收敛到最大化非中心参数的设计。此外，我们通过仿真研究证实了我们的理论发现，该研究涉及对数类样比率统计的渐近和确切功能的计算。
We consider the problem of designing experiments to detect the presence of a specified heteroscedastity in a non-linear Gaussian regression model. In this framework, we focus on the ${\rm D}_s$- and KL-criteria and study their relationship with the noncentrality parameter of the asymptotic chi-squared distribution of a likelihood-based test, for local alternatives. Specifically, we found that when the variance function depends just on one parameter, the two criteria coincide asymptotically and in particular, the ${\rm D}_1$-criterion is proportional to the noncentrality parameter. Differently, if the variance function depends on a vector of parameters, then the KL-optimum design converges to the design that maximizes the noncentrality parameter. Furthermore, we confirm our theoretical findings through a simulation study concerning the computation of asymptotic and exact powers of the log-likelihood ratio statistic.
