logcondens: Computations related to univariate log-concave density estimation - Zurich Open Repository and Archive

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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Item Type: Journal Article, refereed, original work 04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI) 610 Medicine & health English 2011 21 Mar 2011 14:00 05 Apr 2016 14:53 American Statistical Association 1548-7660 http://www.jstatsoft.org/v39/i06