Partially Linear Additive Regression with a General Hilbertian Response
本文针对响应变量取值于一般希尔伯特空间的情形，开发了拟合部分线性可加模型的半参数回归技术，证明了参数分量估计的相合性和渐近正态性，以及非参数分量估计达到单变量收敛速度。
In this article we develop semiparametric regression techniques for fitting partially linear additive models. The methods are for a general Hilbert-space-valued response. They use a powerful technique of additive regression in profiling out the additive nonparametric components of the models, which necessarily involves additive regression of the nonadditive effects of covariates. We show that the estimators of the parametric components are n-consistent and asymptotically Gaussian under weak conditions. We also prove that the estimators of the nonparametric components, which are random elements taking values in a space of Hilbert-space-valued maps, achieve the univariate rate of convergence regardless of the dimension of covariates. We present some numerical evidence for the success of the proposed method and discuss real data applications. Supplementary materials for this article are available online.