Semiparametric regression with localized Bregman divergence
本文研究通过最小化局部化Bregman散度来进行半参数回归，利用广义线性模型框架下的局部参数模型，并探讨了估计量的渐近性质，模拟和实际数据应用表明该回归估计器有效。
Abstract This paper focuses on semiparametric regression based on minimizing the localized Bregman divergence. A local parametric model derived from the framework of the generalized linear model with multiple covariates and a linear predictor is utilized. The parameter vector included in the model is estimated under localization. The asymptotic behavior of both the locally estimated parameter vector and the induced regression estimator is investigated. Theoretical comparisons of estimators by using the divergence risk measure are also addressed. Further generalization, including a multivariate polynomial predictor, is explored, where Faa di Bruno's theorem concerning the derivative of a composition of multivariate functions is efficiently utilized. Simulations and application to a real dataset demonstrate that the proposed regression estimator works efficiently.