LogConcDEAD (version 1.2-0)

LogConcDEAD-package: Maximum likelihood estimation of a log-concave density in arbitrary dimensions

Description

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.

Details

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.

References

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

See Also

logcondens rgl

Examples

#example with some simple normal data

set.seed(101)
x <- matrix(rnorm(200),ncol=2)
out <- lcd.mle(x)
plot(out,itype="ic")