数学
真线性模型
函数导数
局部回归
线性形式
标量(数学)
应用数学
回归分析
估计员
线性回归
统计
非参数回归
回归
数学优化
贝叶斯多元线性回归
多项式回归
功能数据分析
数学分析
几何学
作者
Frédéric Ferraty,Stanislav Nagy
出处
期刊:Biometrika
[Oxford University Press]
日期:2021-04-21
卷期号:109 (2): 439-455
被引量:5
标识
DOI:10.1093/biomet/asab027
摘要
Summary It is common to want to regress a scalar response on a random function. This paper presents results that advocate local linear regression based on a projection as a nonparametric approach to this problem. Our asymptotic results demonstrate that functional local linear regression outperforms its functional local constant counterpart. Beyond the estimation of the regression operator itself, local linear regression is also a useful tool for predicting the functional derivative of the regression operator, a promising mathematical object in its own right. The local linear estimator of the functional derivative is shown to be consistent. For both the estimator of the regression functional and the estimator of its derivative, theoretical properties are detailed. On simulated datasets we illustrate good finite-sample properties of the proposed methods. On a real data example of a single-functional index model, we indicate how the functional derivative of the regression operator provides an original, fast and widely applicable estimation method.
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