LogConcDEAD-package {LogConcDEAD} | R Documentation |
This package contains a function to compute the maximum likelihood estimator of a log-concave density in any number of dimensions using Shor's r-algorithm.
Functions to plot (for 1- and 2-d data) and draw samples from the MLE are provided.
lcd.mle
computes the MLE (specified via its value at data points).
Output is a list of class "LogConcDEAD"
which is used for plotting,
function evaluation etc.
lcd.eval
evaluates the MLE at a particular point.
lcd.sample
draws samples from the MLE.
lcd.interp
interpolates the MLE on a grid, for plotting
purposes.
lcd.marg
integrates the MLE in 2-d to allow plotting of
estimates of (currently only axis-aligned) marginals.
plot.LogConcDEAD
produces plots of the MLE, optionally
using the rgl package.
The authors gratefully acknowledge the assistance of Lutz Duembgen at the University of Bern for his insight into the objective function in lcd.mle
For one dimensional data, the active set algorithm in logcondens is much faster.
Madeleine Cule mlc40@cam.ac.uk
Robert Gramacy bobby@statslab.cam.ac.uk
Richard Samworth rjs57@cam.ac.uk
Maintainer: Madeleine Cule mlc40@cam.ac.uk
Cule, M. L., Samworth, R. J. and Stewart, M. I. (2007) Computing the maximum likelihood estimator of a log-concave density In preparation
Kappel, F. and Kuntsevich, A. V. (2000) An implementation of Shor's r-algorithm Computational Optimization and Applications 15(2) p. 193-205
http://www.uni-graz.at/imawww/kuntsevich/solvopt/
Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T. (1996) The Quickhull algorithm for convex hulls ACM Trans. on Mathematical Software, 22(4) p. 469-483 http://www.qhull.org
#example with some simple normal data set.seed(101) x <- matrix(rnorm(200),ncol=2) out <- lcd.mle(x) plot(out,itype="ic")