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Nonparametric density estimation under unimodality and monotonicity constraints


Cheng, Ming-Yen; Gasser, Theo; Hall, Peter (1999). Nonparametric density estimation under unimodality and monotonicity constraints. Journal of Computational and Graphical Statistics, 8(1):1-21.

Abstract

We introduce a recursive method for estimating a probability density subject to constraints of unimodality or monotonicity. It uses an empirical estimate of the probability transform to construct a sequence of maps of a known template, which satisfies the constraints. The algorithm may be employed without a smoothing step, in which case it produces step-function approximations to the sampling density. More satisfactorily, a certain amount of smoothing may be interleaved between each recursion, in which case the estimate is smooth. The amount of smoothing may be chosen using a standard cross-validation algorithm. Unlike other methods for density estimation, however, the recursive approach is robust against variation of the amount of smoothing, and so choice of bandwidth is not critical.

Abstract

We introduce a recursive method for estimating a probability density subject to constraints of unimodality or monotonicity. It uses an empirical estimate of the probability transform to construct a sequence of maps of a known template, which satisfies the constraints. The algorithm may be employed without a smoothing step, in which case it produces step-function approximations to the sampling density. More satisfactorily, a certain amount of smoothing may be interleaved between each recursion, in which case the estimate is smooth. The amount of smoothing may be chosen using a standard cross-validation algorithm. Unlike other methods for density estimation, however, the recursive approach is robust against variation of the amount of smoothing, and so choice of bandwidth is not critical.

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66 citations in Web of Science®
13 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:610 Medicine & health
Language:English
Date:1999
Deposited On:08 Aug 2016 06:46
Last Modified:08 Aug 2016 06:46
Publisher:American Statistical Association
ISSN:1061-8600
Publisher DOI:https://doi.org/10.1080/10618600.1999.10474798

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