文章基本信息

标题：Nonparametric regression to the mean
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作者：Hans-Georg Müller ; Ian Abramson ; Rahman Azari 等
期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2003
卷号：100
期号：17
页码：9715-9720
DOI：10.1073/pnas.1733547100
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Available data may reflect a true but unknown random variable of interest plus an additive error, which is a nuisance. The problem in predicting the unknown random variable arises in many applied situations where measurements are contaminated with errors; it is known as the regression-to-the-mean problem. There exists a well known solution when both the distributions of the true underlying random variable and the contaminating errors are normal. This solution is given by the classical regression-to-the-mean formula, which has a data-shrinkage interpretation. We discuss the extension of this solution to cases where one or both of these distributions are unknown and demonstrate that the fully nonparametric case can be solved for the case of small contaminating errors. The resulting nonparametric regression-to-the-mean paradigm can be implemented by a straightforward data-sharpening algorithm that is based on local sample means. Asymptotic justifications and practical illustrations are provided.