LogConcDEAD-package {LogConcDEAD}R Documentation

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.

Note

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.

Author(s)

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

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")

[Package LogConcDEAD version 1.1-2 Index]