logconcens-package {logconcens}

Maximum Likelihood Estimation of a Log-Concave Density Based on Censored Data

Description

Based on independent intervals X_i = [L_i,R_i], where -\infty < L_i \leq R_i \leq \infty, compute the maximum likelihood estimator of a (sub)probability density under the assumption that it is log-concave. For further information see Duembgen, Rufibach, and Schuhmacher (2013).

Details

The main function is logcon, which offers computation of the MLE for many types of censored and also exact data. Various parameters can be set that allow for fine control of the underlying EM algorithm in “difficult” situations. An object of type lcdensity is returned, for which plot, print, and summary methods are available. There is also a function loglike for computing the log-likelihood of a lcdensity object.

Author(s)

Dominic Schuhmacher [e-mail]
Kaspar Rufibach [e-mail]
Lutz Duembgen [e-mail]

Maintainer: Dominic Schuhmacher [e-mail]

References

Duembgen, L., Rufibach, K., and Schuhmacher, D. (2014). Maximum-likelihood estimation of a log-concave density based on censored data. Electronic Journal of Statistics, 8(1), 1405-1437. doi:10.1214/14-EJS930

Examples

## Simple examples with simulated data.
## For more detailed examples see the help for the function logcon.

## exact data
set.seed(10)
x <- rnorm(100)
res <- logcon(x)
## Not run: 
plot(res)
xi <- seq(-3,3,0.05)
lines(xi,log(dnorm(xi)))
## End(Not run)

## interval censored data
x <- rgamma(50,3,1)
x <- cbind(x,x+rexp(50,1))
plotint(x)
res <- logcon(x)
## Not run: plot(res, type="CDF")

## right censored data with mass at infinity
set.seed(11)
x <- rgamma(50,3,1)
x <- cbind(x,ifelse(rexp(50,1/3) < x,Inf,x))
plotint(x)
res <- logcon(x,adapt.p0=TRUE)
## Not run: plot(res, type="survival")

## rounded/binned data
set.seed(12)
x <- round(rnorm(100))
x <- cbind(x-0.5,x+0.5)
plotint(x)
res <- logcon(x)
## Not run: 
plot(res)
xi <- seq(-3,3,0.05)
lines(xi,log(dnorm(xi)))
## End(Not run)