Local linear fitting and improved estimation near peaks. (English) Zbl 1177.62048

Summary: The authors look into the problem of estimating regression functions that exhibit jump irregularities in the first derivative. They investigate the behaviour of the bias in the local linear fit and show the superior performance of appropriate one-sided versions of the local linear fit near such irregularities. They then propose an improved estimation procedure based on data-driven selection of a conventional or one-sided local linear fit according to a residual sum of squares type of criterion. The authors provide theoretical results and illustrate the method both on simulated and real-life data examples.


62G08 Nonparametric regression and quantile regression
65C60 Computational problems in statistics (MSC2010)


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