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.

AuthorKaspar Rufibach <kaspar.rufibach@gmail.com> and Lutz Duembgen <duembgen@stat.unibe.ch>
Date of publication2016-07-14 00:31:11
MaintainerKaspar Rufibach <kaspar.rufibach@gmail.com>
LicenseGPL (>= 2)
Version2.1.5
http://www.kasparrufibach.ch , http://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html

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

Functions

activeSet Man page
activeSetLogCon Man page
activeSetRoutines Man page
brightstar Man page
c2hat Man page
confIntBootLogConROC_t0 Man page
etaphi Man page
evaluateLogConDens Man page
ftilde Man page
icmaLogCon Man page
intECDF Man page
intF Man page
isoMean Man page
J00 Man page
J10 Man page
J11 Man page
J20 Man page
Jfunctions Man page
Lhat_eta Man page
LocalCoarsen Man page
LocalConvexity Man page
LocalExtend Man page
LocalF Man page
Local_LL Man page
Local_LL_all Man page
LocalMLE Man page
LocalNormalize Man page
LocalVariance Man page
logcon Man page
log-concave Man page
logConCI Man page
logConCIfunctions Man page
logcondens Man page
logConDens Man page
logcon-package Man page
logConROC Man page
logconTwoSample Man page
maxDiffCDF Man page
MLE Man page
pancreas Man page
phieta Man page
plot.dlc Man page
preProcess Man page
Q00 Man page
qloglin Man page
quadDeriv Man page
quantilesLogConDens Man page
reliability Man page
reparametrizations Man page
rLCD Man page
rlogcon Man page
robust Man page
ROCx Man page
summary.dlc Man page

Files

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

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