在Copula回归模型中检验正确的模型设定
Testing for correct model specification in copula regression models
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中文总结 AI 辅助
针对半参数Copula回归模型，通过引入真实回归函数与假定模型中最佳逼近的加权\(L^2\)距离进行拟合优度检验，推导检验方法并构建置信区间，有限样本模拟显示该方法有良好性质。
中文摘要 AI 辅助
我们为半参数Copula回归模型提出了一个拟合优度检验。这类模型根据边际分布函数和Copula密度来表达回归函数，为避免高维回归问题中的完全非参数估计提供了灵活方式。但其性能关键取决于参数Copula族的设定。我们不是检验Copula模型本身，而是直接在诱导回归函数层面评估误设。为此引入了真实回归函数与其在假定Copula回归模型中的最佳逼近之间的加权\(L^2\)距离。提出了该距离的核估计量，并证明在正确设定的原假设和固定备择假设下是一致且渐近正态的。我们推导了经典设定检验，并使用自归一化序贯统计量构建了关键置信区间以及针对与模型相关偏差的检验。有限样本模拟证明了所提方法有准确的水平逼近和良好的功效性质。
英文摘要
We propose a goodness-of-fit test for semiparametric copula regression models. Such models express the regression function in terms of marginal distribution functions and copula densities and therefore provide a flexible way to avoid fully nonparametric estimation in high-dimensional regression problems. Their performance, however, depends crucially on the specification of the parametric copula family. Instead of testing the copula model itself, we assess misspecification directly at the level of the induced regression function. To this end, we introduce a weighted $L^2$-distance between the true regression function and its best approximation within the postulated copula regression model. A kernel-based estimator of this distance is proposed and shown to be consistent and asymptotically normal under both the null hypothesis of correct specification and fixed alternatives. We derive a classical specification test and, using a self-normalized sequential statistic, construct pivotal confidence intervals and tests for relevant deviations from the model. Finite-sample simulations demonstrate accurate level approximation and good power properties of the proposed procedures.
