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), evaluate and draw samples from the maximum likelihood estimator are provided.
This package contains a selection of functions for maximum likelihood estimation under the constraint of log-concavity.
mlelcd
computes the maximum likelihood estimator
(specified via its value at data points). Output is a list of class
"LogConcDEAD"
which is used as input to various auxiliary functions.
dlcd
evaluates the estimated density at a particular point.
rlcd
draws samples from the estimated density.
interplcd
interpolates the estimated density on
a grid for plotting purposes.
dmarglcd
evaluates the estimated marginal density by
integrating the estimated density over an appropriate subspace.
interpmarglcd
evaluates a marginal density estimate at
equally spaced points along the axis for plotting purposes. This is
done by integrating the estimated density over an appropriate subspace.
plot.LogConcDEAD
produces plots of the maximum likelihood
estimator, optionally using the rgl package.
print
and
summary
methods are also available.
The authors gratefully acknowledge the assistance of Lutz Duembgen at the University of Bern for his insight into the objective function in mlelcd.
For one dimensional data, the active set algorithm in logcondens is much faster.
Madeleine Cule (maintainer) mlc40@cam.ac.uk
Robert Gramacy bobby@statslab.cam.ac.uk
Richard Samworth rjs57@cam.ac.uk
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
Cule, M. L. and D"umbgen, L. (2008) On an auxiliary function for log-density estimation, University of Bern technical report. http://arxiv.org/abs/0807.4719
Cule, M. L., Samworth, R. J., and Stewart, M. I. (2007) Maximum likelihood estimation of a log-concave density, Submitted.http://arxiv.org/abs/0804.3989
Kappel, F. and Kuntsevich, A. V. (2000)
An implementation of Shor's r-algorithm Computational
Optimization and Applications 15
http://www.uni-graz.at/imawww/kuntsevich/solvopt/
Shor, N. Z. (1985) Minimization methods for nondifferentiable functions Springer-Verlag
## Some simple normal data, and a few plots x <- matrix(rnorm(200),ncol=2) lcd <- mlelcd(x) g <- interplcd(lcd) par(mfrow=c(2,2), ask=TRUE) plot(lcd, g=g, type="c") plot(lcd, g=g, type="c", uselog=TRUE) plot(lcd, g=g, type="i") plot(lcd, g=g, type="i", uselog=TRUE) ## Some plots of marginal estimates par(mfrow=c(1,1)) g.marg1 <- interpmarglcd(lcd, marg=1) g.marg2 <- interpmarglcd(lcd, marg=2) plot(lcd, marg=1, g.marg=g.marg1) plot(lcd, marg=2, g.marg=g.marg2) ## generate some points from the fitted density generated <- rlcd(100, lcd) genmean <- mean(generated) ## evaluate the fitted density mypoint <- c(0, 0) dlcd(mypoint, lcd, uselog=FALSE) mypoint <- c(10, 0) dlcd(mypoint, lcd, uselog=FALSE) ## evaluate the marginal density dmarglcd(0, lcd, marg=1) dmarglcd(1, lcd, marg=2)