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首页> 外文期刊>Proceedings of the National Academy of Sciences of the United States of America >Nonparametric regression to the mean.
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Nonparametric regression to the mean.

机译：非参数回归均值。

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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.
机译：可用数据可能反映了一个真实但未知的目标随机变量以及一个累加误差，该误差是令人讨厌的。预测未知随机变量的问题出现在许多应用场合中，其中测量值被误差污染。它被称为均值回归问题。当真实的基础随机变量的分布和污染误差都为正态时，存在一种众所周知的解决方案。该解决方案由经典的均值回归公式给出，该公式具有数据收缩解释。我们讨论了将该解决方案扩展到其中一个或两个分布未知的情况，并证明对于小污染误差的情况，可以解决完全非参数的情况。可以通过基于局部样本均值的简单数据锐化算法来实现最终的非参数均值回归范式。提供渐近论证和实际例证。

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