Local_LL_all

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

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

Some vector ${\bold{\phi}}$ of the same length as ${\bold{x}}$ and ${\bold{w}}$.

Computes the value of the log-likelihood function

  $$L(\phi) = \sum_{i=1}^m w_i \phi(x_i) - \int_{x_1}^{x_m} \exp(\phi(t)) dt,$$

a new candidate for $\phi$ via the Newton method as well as the directional derivative of ${\bold{\phi}} \to L({\bold{\phi}})$ 
into that direction.

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.

Local_LL_all: Log-likelihood, New Candidate and Directional Derivative for L

Description

Usage

Arguments

Value