Vector of independent and identically distributed numbers, with strictly increasing entries.

Optional vector of nonnegative weights corresponding to ${\bold{x}_m}$.

phi_o

Threshold for the directional derivative during the Newton-Raphson procedure.

prec

print = TRUE outputs log-likelihood in every loop, print = FALSE does not. Make sure to tell R to output (press CTRL+W).

print

Given a vector of observations ${\bold{x}} = (x_1, \ldots, x_m)$ with pairwise distinct entries and
a vector of weights ${\bold{w}}=(w_1, \ldots, w_m)$ s.t. $\sum_{i=1}^m w_i = 1$, this function computes a function $\widehat \phi_{MLE}$ (represented by the vector $(\widehat \phi_{MLE}(x_i))_{i=1}^m$) supported by $[x_1, x_m]$ such that 

$$L(\phi) = \sum_{i=1}^m w_i \phi(x_i) - \sum_{j=1}^{m-1} (x_{j+1} - x_j) J(\phi_j, \phi_{j+1})$$

is maximal over all continuous, piecewise linear functions with knots in ${x_1, \ldots, x_m}$

htest

nonparametric

Given independent and identically distributed observations X(1), ..., X(n), this package allows to 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. Finally, three datasets that have been used to illustrate log-concave density estimation are made available.

MLE: Unconstrained piecewise linear MLE

Description

Usage

Arguments

Value