This function is used in the computation of \(\widehat f^*\) and \(\widehat F^*\).

htest

nonparametric

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.

Kaspar Rufibach

logcondens

Estimate a Log-Concave Probability Density from Iid Observations

Q00 function

<dl> <dt>x</dt>
<dd>Number at which to compute \(q\) and/or \(Q\).</dd> <dt>a</dt>
<dd>Vector of length \(m\) with real entries.</dd> <dt>u</dt>
<dd>Vector of length \(m\) with real entries.</dd> <dt>v</dt>
<dd>Vector of length \(m\) with real entries.</dd> <dt>gamma</dt>
<dd>Real number. Standard deviation to be used.</dd> <dt>QFhat</dt>
<dd>Logical. Should \(Q\) be computed?</dd></dl>

Arguments

Kaspar Rufibach, <a href="/link/kaspar.rufibach%40gmail.com?package=logcondens&version=2.1.8" data-mini-rdoc="logcondens::kaspar.rufibach@gmail.com">kaspar.rufibach@gmail.com</a>, <a href="http://www.kasparrufibach.ch">http://www.kasparrufibach.ch</a>
Lutz Duembgen, <a href="/link/duembgen%40stat.unibe.ch?package=logcondens&version=2.1.8" data-mini-rdoc="logcondens::duembgen@stat.unibe.ch">duembgen@stat.unibe.ch</a>, <a href="https://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html">https://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html</a>

Author

Numerical Routine Q — Q00

<dl>

 <dt>x</dt>
<dd>Number at which to compute \(q\) and/or \(Q\).</dd>

 <dt>a</dt>
<dd>Vector of length \(m\) with real entries.</dd>

 <dt>u</dt>
<dd>Vector of length \(m\) with real entries.</dd>

 <dt>v</dt>
<dd>Vector of length \(m\) with real entries.</dd>

 <dt>gamma</dt>
<dd>Real number. Standard deviation to be used.</dd>

 <dt>QFhat</dt>
<dd>Logical. Should \(Q\) be computed?</dd>

</dl>

Kaspar Rufibach, <a href='mailto:kaspar.rufibach@gmail.com'>kaspar.rufibach@gmail.com</a>, <a href='http://www.kasparrufibach.ch'>http://www.kasparrufibach.ch</a>
Lutz Duembgen, <a href='mailto:duembgen@stat.unibe.ch'>duembgen@stat.unibe.ch</a>, <a href='https://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html'>https://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html</a>

Q00: Numerical Routine Q

Description

Usage

Value

Arguments

Author

References