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首页> 外文期刊>Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability >Smooth backfitting for additive modeling with small errors-in-variables, with an application to additive functional regression for multiple predictor functions
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Smooth backfitting for additive modeling with small errors-in-variables, with an application to additive functional regression for multiple predictor functions

机译:适用于少量误差模拟的顺畅的备用,应用于多个预测函数的添加功能回归

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摘要

We study smooth backfitting when there are errors-in-variables, which is motivated by functional additive models for a functional regression model with a scalar response and multiple functional predictors that are additive in the functional principal components of the predictor processes. The development of a new smooth backfitting technique for the estimation of the additive component functions in functional additive models with multiple functional predictors requires to address the difficulty that the eigenfunctions and therefore the functional principal components of the predictor processes, which are the arguments of the proposed additive model, are unknown and need to be estimated from the data. The available estimated functional principal components contain an error that is small for large samples but nevertheless affects the estimation of the additive component functions. This error-in-variables situation requires to develop new asymptotic theory for smooth backfitting. Our analysis also pertains to general situations where one encounters errors in the predictors for an additive model, when the errors become smaller asymptotically. We also study the finite sample properties of the proposed method for the application in functional additive regression through a simulation study and a real data example.
机译:当存在错误变量的错误时,我们研究了平稳的回溯,这是通过功能回归模型的功能性添加剂模型的动机,其具有标量响应和在预测器过程的功能主组件中是附加的多个功能预测。在具有多个功能预测器的功能添加剂模型中估计的新的平滑应答技术的开发需要满足特征障碍的难度,因此是预测器过程的功能主要组成部分,这是所提出的拟议的争论添加剂模型是未知的,需要从数据估计。可用估计的功能主体组件包含一个误差对于大型样本很小,但是,影响添加剂组件函数的估计。这种变量错误的情况需要开发新的渐近理论,以实现平稳的支持。我们的分析还涉及一般情况,当错误变得越来越小时,遇到添加剂模型中的预测器中的错误。我们还通过模拟研究和实际数据示例研究了在功能性添加剂回归中的应用方法的有限样本性质。

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