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logcondens: Computations related to univariate log-concave density estimation


Dümbgen, L; Rufibach, K (2011). logcondens: Computations related to univariate log-concave density estimation. Journal of Statistical Software, 39(6):1-28.

Abstract

Maximum likelihood estimation of a log-concave density has attracted considerable attention over the last few years. Several algorithms have been proposed to estimate such
a density. Two of those algorithms, an iterative convex minorant and an active set algorithm, are implemented in the R package logcondens. While these algorithms are discussed elsewhere, we describe in this paper the use of the logcondens package and discuss functions
and datasets related to log-concave density estimation contained in the package. In particular, we provide functions to (1) compute the maximum likelihood estimate (MLE) as well as a smoothed log-concave density estimator derived from the MLE, (2) evaluate the estimated density, distribution and quantile functions at arbitrary points, (3) compute the characterizing functions of the MLE, (4) sample from the estimated distribution, and �nally (5) perform a two-sample permutation test using a modi�ed Kolmogorov-Smirnov test statistic. In addition, logcondens makes two datasets available that have been used
to illustrate log-concave density estimation.

Abstract

Maximum likelihood estimation of a log-concave density has attracted considerable attention over the last few years. Several algorithms have been proposed to estimate such
a density. Two of those algorithms, an iterative convex minorant and an active set algorithm, are implemented in the R package logcondens. While these algorithms are discussed elsewhere, we describe in this paper the use of the logcondens package and discuss functions
and datasets related to log-concave density estimation contained in the package. In particular, we provide functions to (1) compute the maximum likelihood estimate (MLE) as well as a smoothed log-concave density estimator derived from the MLE, (2) evaluate the estimated density, distribution and quantile functions at arbitrary points, (3) compute the characterizing functions of the MLE, (4) sample from the estimated distribution, and �nally (5) perform a two-sample permutation test using a modi�ed Kolmogorov-Smirnov test statistic. In addition, logcondens makes two datasets available that have been used
to illustrate log-concave density estimation.

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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:2011
Deposited On:21 Mar 2011 14:00
Last Modified:21 Nov 2017 15:22
Publisher:American Statistical Association
ISSN:1548-7660
Official URL:http://www.jstatsoft.org/v39/i06

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