Nonparametric Estimation of the Conditional Distribution at Regression Boundary Points
Nonparametric Estimation of the Conditional Distribution at Regression Boundary Points
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DOI：
10.1080/00031305.2018.1558109
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发表时间：
2017-04
期刊：
影响因子：
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通讯作者：
Srinjoy Das;D. Politis
中科院分区：
文献类型：
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作者：
Srinjoy Das;D. Politis
摘要非参数回归是一种标准的统计工具，在大数据时代越来越重要。边界点造成额外的困难，但局部多项式回归可以用来减轻它们。例如，局部线性回归很容易实现，并且在内部和边界点上都表现得很好。估计条件分布函数和/或分位数函数在一个给定的回归点是立即通过标准的内核方法，但问题随之而来，如果要使用局部线性方法。特别是，分布函数估计量不能保证是单调递增的，并且分位数曲线可以“交叉”。本文提出了一种修正局部线性分布估计单调性的简单方法，并通过模拟和真实的数据实例证明了其良好的性能。本文的补充材料可在网上查阅。
Abstract Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for example, is easy to implement and performs quite well both at interior and boundary points. Estimating the conditional distribution function and/or the quantile function at a given regressor point is immediate via standard kernel methods but problems ensue if local linear methods are to be used. In particular, the distribution function estimator is not guaranteed to be monotone increasing, and the quantile curves can “cross.” In the article at hand, a simple method of correcting the local linear distribution estimator for monotonicity is proposed, and its good performance is demonstrated via simulations and real data examples. Supplementary materials for this article are available online.