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Estimation of irregular probability densities

Lieven Desmet, Irène Gijbels, and Alexandre Lambert

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This paper deals with nonparametric estimation of an unknown density function which possibly is discontinuous or non-differentiable in an unknown finite number of points. Estimation of such irregular densities is accomplished by viewing the problem as a regression problem and applying recent techniques for estimation of irregular regression curves. Moreover, the method can deal with estimation of densities that have an irregularity at the endpoint(s) of their support. A simulation study compares the performance of the proposed method with those of other methods available in the literature. A further illustration on real data is provided.

Chapter information

J. Antoch, M. Hušková and P.K. Sen, eds., Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis: A Festschrift in honor of Professor Jana Jurečková (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2010), 46-61

First available in Project Euclid: 29 November 2010

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 62G07: Density estimation
Secondary: 62G08: Nonparametric regression

density estimation irregularities local linear fitting variance stabilization

Copyright © 2010, Institute of Mathematical Statistics


Desmet, Lieven; Gijbels, Irène; Lambert, Alexandre. Estimation of irregular probability densities. Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis: A Festschrift in honor of Professor Jana Jurečková, 46--61, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2010. doi:10.1214/10-IMSCOLL705.

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