Regression function estimation on non compact support in an heteroscesdastic model

被引：5

作者：

Comte, F. ^{[1
]}

Genon-Catalot, V. ^{[1
]}

机构：

[1] Univ Paris 05, Lab MAP5, CNRS, UMR 8145, Paris, France

来源：

METRIKA | 2020年 / 83卷 / 01期

关键词：

Heteroscedatic regression model; Least squares estimation; Model selection; Projection estimator; LAGUERRE; BOUNDS;

D O I：

10.1007/s00184-019-00727-4

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We study the problem of nonparametric regression function estimation on non necessarily compact support in a heteroscedastic model with non necessarily bounded variance. A collection of least squares projection estimators on m-dimensional functional linear spaces is built. We prove new risk bounds for the estimator with fixed m and propose a new selection procedure relying on inverse problems methods leading to an adaptive estimator. Contrary to more standard cases, the data-driven dimension is chosen within a random set and the penalty is random. Examples and numerical simulations results show that the procedure is easy to implement and provides satisfactory estimators.

引用

页码：93 / 128

页数：36