In this paper we discuss the estimation of a fairly general type of varying coefficient model. The model is for a response variable that takes values in a general Hilbert space and allows for various types of additive interaction terms in representing the effects of predictors. It also accommodates both continuous and discrete predictors. We develop a powerful technique of estimating the very general model. Our approach may be used in a variety of situations where one needs to analyze the relation between a set of predictors and a Hilbertian response. We prove the existence of the estimators of the model itself and of its components, and also the convergence of a backfitting algorithm that realizes the estimators. We derive the rates of convergence of the estimators and their asymptotic distributions. We also demonstrate via simulation study that our approach works efficiently, and illustrate its usefulness through a real data application.

中文翻译：

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希尔伯变系数模型的估计

在本文中，我们讨论了一种相当一般类型的变系数模型的估计。该模型适用于一个响应变量，该变量在一般希尔伯特空间中取值，并允许在表示预测变量的影响时使用各种类型的加性交互项。它还适用于连续和离散的预测变量。我们开发了一种强大的技术来估计非常通用的模型。我们的方法可用于需要分析一组预测变量和希尔伯特响应之间的关系的各种情况。我们证明了模型本身及其组件的估计器的存在，以及实现估计器的后拟合算法的收敛性。我们推导出估计量的收敛率及其渐近分布。