logcondens: Estimate a Log-Concave Probability Density from Iid Observations

Given independent and identically distributed observations X(1), ..., X(n), compute the maximum likelihood estimator (MLE) of a density as well as a smoothed version of it under the assumption that the density is log-concave, see Rufibach (2007) and Duembgen and Rufibach (2009). The main function of the package is 'logConDens' that allows computation of the log-concave MLE and its smoothed version. In addition, we provide functions to compute (1) the value of the density and distribution function estimates (MLE and smoothed) at a given point (2) the characterizing functions of the estimator, (3) to sample from the estimated distribution, (5) to compute a two-sample permutation test based on log-concave densities, (6) the ROC curve based on log-concave estimates within cases and controls, including confidence intervals for given values of false positive fractions (7) computation of a confidence interval for the value of the true density at a fixed point. Finally, three datasets that have been used to illustrate log-concave density estimation are made available.

Author
Kaspar Rufibach <kaspar.rufibach@gmail.com> and Lutz Duembgen <duembgen@stat.unibe.ch>
Date of publication
2016-07-14 00:31:11
Maintainer
Kaspar Rufibach <kaspar.rufibach@gmail.com>
License
GPL (>= 2)
Version
2.1.5
URLs

View on CRAN

Man pages

activeSetLogCon
Computes a Log-Concave Probability Density Estimate via an...
activeSetRoutines
Auxiliary Numerical Routines for the Function activeSetLogCon
brightstar
Bright star dataset used to illustrate log-concave density...
confIntBootLogConROC_t0
Function to compute a bootstrap confidence interval for the...
evaluateLogConDens
Evaluates the Log-Density MLE and Smoothed Estimator at...
icmaLogCon
Computes a Log-Concave Probability Density Estimate via an...
intECDF
Computes the Integrated Empirical Distribution Function at...
intF
Computes the Integral of the estimated CDF at Arbitrary Real...
isoMean
Pool-Adjacent Violaters Algorithm: Least Square Fit under...
Jfunctions
Numerical Routine J and Some Derivatives
Lhat_eta
Value of the Log-Likelihood Function L, where Input is in...
Local_LL
Value of the Log-Likelihood Function L, where Input is in...
Local_LL_all
Log-likelihood, New Candidate and Directional Derivative for...
logConCI
Compute pointwise confidence interval for a density assuming...
logConCIfunctions
Functions that are used by logConCI
logConDens
Compute log-concave density estimator and related quantities
logcondens-package
Estimate a Log-Concave Probability Density from iid...
logConROC
Compute ROC curve based on log-concave estimates for the...
logconTwoSample
Compute p-values for two-sample test based on log-concave CDF...
maxDiffCDF
Compute maximal difference between CDFs corresponding to...
MLE
Unconstrained piecewise linear MLE
pancreas
Data from pancreatic cancer serum biomarker study
plot.dlc
Standard plots for a dlc object
preProcess
Compute a weighted sample from initial observations
Q00
Numerical Routine Q
qloglin
Quantile Function In a Simple Log-Linear model
quadDeriv
Gradient and Diagonal of Hesse Matrix of Quadratic...
quantilesLogConDens
Function to compute Quantiles of Fhat
reliability
Reliability dataset used to illustrate log-concave density...
reparametrizations
Changes Between Parametrizations
rlogcon
Generate random sample from the log-concave and the smoothed...
robust
Robustification and Hermite Interpolation for ICMA
ROCx
Compute ROC curve at a given x based on log-concave estimates...
summary.dlc
Summarizing log-concave density estimation

Files in this package

logcondens
logcondens/inst
logcondens/inst/CITATION
logcondens/inst/doc
logcondens/inst/doc/logcondens.Rnw
logcondens/inst/doc/logcondens.pdf
logcondens/inst/doc/logcondens.R
logcondens/NAMESPACE
logcondens/NEWS
logcondens/data
logcondens/data/reliability.rda
logcondens/data/brightstar.rda
logcondens/data/pancreas.rda
logcondens/R
logcondens/R/intF.r
logcondens/R/qloglin.r
logcondens/R/rlogcon.r
logcondens/R/Local_LL.r
logcondens/R/confIntBootLogConROC_t0.r
logcondens/R/LocalVariance.r
logcondens/R/LocalF.r
logcondens/R/etaphi.r
logcondens/R/J20.r
logcondens/R/maxDiffCDF.r
logcondens/R/phieta.r
logcondens/R/c2hat.R
logcondens/R/evaluateLogConDens.r
logcondens/R/J11.r
logcondens/R/Q00.r
logcondens/R/summary.dlc.r
logcondens/R/activeSetLogCon.r
logcondens/R/LocalConvexity.r
logcondens/R/Lhat_eta.r
logcondens/R/MLE.r
logcondens/R/isoMean.r
logcondens/R/logconTwoSample.r
logcondens/R/logConROC.R
logcondens/R/robust.r
logcondens/R/LocalMLE.r
logcondens/R/intECDF.r
logcondens/R/J10.r
logcondens/R/logConCI.R
logcondens/R/quantilesLogConDens.r
logcondens/R/preProcess.r
logcondens/R/Local_LL_all.r
logcondens/R/ftilde.r
logcondens/R/LocalNormalize.r
logcondens/R/plot.dlc.r
logcondens/R/ROCx.r
logcondens/R/LocalExtend.r
logcondens/R/logConDens.r
logcondens/R/LocalCoarsen.r
logcondens/R/icmaLogCon.r
logcondens/R/quadDeriv.r
logcondens/R/rLCD.R
logcondens/R/J00.r
logcondens/vignettes
logcondens/vignettes/logcondens.Rnw
logcondens/vignettes/plots
logcondens/vignettes/plots/-plot2.pdf
logcondens/vignettes/plots/-plot2sample.pdf
logcondens/vignettes/plots/-sim1.pdf
logcondens/vignettes/plots/-plot1.pdf
logcondens/vignettes/plots/-plotSimul.pdf
logcondens/vignettes/results
logcondens/vignettes/results/pvals_setting=3_n1=20_n2=25_tau=1.txt
logcondens/vignettes/results/pvals_setting=1_n1=20_n2=25_mu1=0_mu2=1.5.txt
logcondens/vignettes/results/pvals_setting=2_n1=20_n2=25_mu1=0_mu2=0.5.txt
logcondens/vignettes/results/pvals_setting=1_n1=20_n2=25_mu1=0_mu2=0.5.txt
logcondens/vignettes/results/pvals_setting=2_n1=20_n2=25_mu1=0_mu2=1.txt
logcondens/vignettes/results/pvals_setting=3_n1=20_n2=25_tau=2.5.txt
logcondens/vignettes/results/pvals_setting=1_n1=20_n2=25_mu1=0_mu2=1.txt
logcondens/vignettes/results/pvals_setting=2_n1=20_n2=25_mu1=0_mu2=2.txt
logcondens/vignettes/results/pvals_setting=2_n1=20_n2=25_mu1=0_mu2=1.5.txt
logcondens/vignettes/results/pvals_setting=1_n1=20_n2=25_mu1=0_mu2=2.txt
logcondens/vignettes/results/pvals_setting=1_n1=20_n2=25_mu1=0_mu2=0.txt
logcondens/vignettes/results/pvals_setting=3_n1=20_n2=25_tau=3.txt
logcondens/vignettes/results/pvals_setting=3_n1=20_n2=25_tau=1.5.txt
logcondens/vignettes/results/pvals_setting=3_n1=20_n2=25_tau=2.txt
logcondens/vignettes/results/pvals_setting=2_n1=20_n2=25_mu1=0_mu2=0.txt
logcondens/vignettes/stat.bib
logcondens/vignettes/jss.dtx
logcondens/vignettes/jsslogo.jpg
logcondens/MD5
logcondens/build
logcondens/build/vignette.rds
logcondens/DESCRIPTION
logcondens/man
logcondens/man/reparametrizations.Rd
logcondens/man/brightstar.Rd
logcondens/man/logconTwoSample.Rd
logcondens/man/pancreas.Rd
logcondens/man/quadDeriv.Rd
logcondens/man/isoMean.Rd
logcondens/man/Lhat_eta.Rd
logcondens/man/Jfunctions.Rd
logcondens/man/preProcess.Rd
logcondens/man/activeSetRoutines.Rd
logcondens/man/confIntBootLogConROC_t0.Rd
logcondens/man/logConCI.Rd
logcondens/man/maxDiffCDF.Rd
logcondens/man/logConCIfunctions.Rd
logcondens/man/robust.Rd
logcondens/man/plot.dlc.Rd
logcondens/man/icmaLogCon.Rd
logcondens/man/intECDF.Rd
logcondens/man/reliability.Rd
logcondens/man/qloglin.Rd
logcondens/man/summary.dlc.Rd
logcondens/man/logConROC.Rd
logcondens/man/activeSetLogCon.Rd
logcondens/man/Q00.Rd
logcondens/man/evaluateLogConDens.Rd
logcondens/man/logConDens.Rd
logcondens/man/Local_LL_all.Rd
logcondens/man/quantilesLogConDens.Rd
logcondens/man/rlogcon.Rd
logcondens/man/MLE.Rd
logcondens/man/ROCx.Rd
logcondens/man/logcondens-package.Rd
logcondens/man/intF.Rd
logcondens/man/Local_LL.Rd