rslcd: Sample from a smoothed log-concave maximum likelihood estimate

Description

Draws samples from a smoothed log-concave maximum likelihood estimate. The estimate should be specified in the form of an object of class "LogConcDEAD", the result of a call to mlelcd, and a positive definite matrix.

Usage

rslcd(n=1, lcd, A=hatA(lcd), method=c("Independent","MH"))

Arguments

A scalar integer indicating the number of samples required

lcd

Object of class "LogConcDEAD" (typically output from mlelcd)

A positive definite matrix that determines the degree of smoothing, typically taken as the output of hatA(lcd)

method

Indicator of the method used to draw samples, either via independent rejection sampling (default choice) or via Metropolis-Hastings

Value

A numeric matrix with n rows, each row corresponding to a point in $R^d$ drawn from the distribution with density defined by lcd and A.

Details

This function by default uses a simple rejection sampling scheme to draw independent random samples from a smoothed log-concave maximum likelihood estimator. One can also use the Metropolis-Hastings option to draw (dependent) samples with a higher acceptance rate.

For examples, see mlelcd.

References

Chen, Y. and Samworth, R. J. (2012), Smoothed log-concave maximum likelihood estimation with applications Submitted. http://arxiv.org/abs/1102.1191v4

Cule, M. L., Samworth, R. J., and Stewart, M. I. (2010) Maximum likelihood estimation of a multi-dimensional log-concave density J. Roy. Statist. Soc., Ser. B. (with discussion), 72, 545-600.

Gopal, V. and Casella, G. (2010) Discussion of Maximum likelihood estimation of a log-concave density by Cule, Samworth and Stewart J. Roy. Statist. Soc., Ser. B., 72, 580-582.