Fully Data-Driven Nonparametric Variance Estimators
作者:
Michael H. Neumann,
期刊:
Statistics
(Taylor Available online 1994)
卷期:
Volume 25,
issue 3
页码: 189-212
ISSN:0233-1888
年代: 1994
DOI:10.1080/02331889408802445
出版商: Gordon & Breach Science Publishers
关键词: AMS 1991 Mathematics subject classification;Primary 62G07;secondary 62G20;Variance estimation;kernel regression;bandwidth choice;asymptotic efficiency;optimal convergence rate;asymptotic minimax risk
数据来源: Taylor
摘要:
We consider the problem of estimating the unknown variance function υ in a nonparametric regression model. As a basis for our estimators we take estimated residuals which are based on a kernel estimator of the mean vector. Then we form with these residuals a kernel estimator of υ. Main emphasis is on a data-driven choice of the bandwidths involved in the procedure. It is shown that the risk of this estimator attains the uniform convergence rate in Sobolev classes for υ under weak smoothness assumptions on the mean. Moreover, we prove that there is asymptotically no loss due to the estimation of the mean.
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