activeSetLogCon
(Package: logcondens.mode) :
Computes a Log-Concave Probability Density Estimate via an Active Set Algorithm
Given a vector of observations x_n = (x_1, …, x_n) with not necessarily equal entries, activeSetLogCon first computes vectors x_m = (x_1, …, x_m) and w = (w_1, …, w_m) where w_i is the weight of each x_i s.t. ∑_{i=1}^m w_i = 1. Then, activeSetLogCon computes a concave, piecewise linear function widehat φ_m on [x_1, x_m] with knots only in {x_1, …, x_m} such that
Extension of the logcondens package. Computes maximum likelihood estimate of a log-concave density with fixed and known location of the mode. Performs inference about the mode via a likelihood ratio test comparing the unconstrained log-concave estimator to the constrained one.
Compute the confidence interval (CI) for the mode of a log-concave density by "inverting" the likelihood ratio statistic, i.e. the 1-α CI is composed of mode values at which the likelihood ratio test does not reject at the α-level.
Sampling from a given distribution, we estimate via Monte Carlo the limiting distribution of 2-log-likelihood-ratio of the modally-constrained log-concave MLE to the (unconstrained) log-concave MLE.
A likelihood ratio test to test whether mode is the location of the mode of a (log-concave) density. Uses activeSetLogCon and activeSetLogCon.mode to compute the log-concave MLE and the log-concave MLE where the mode is restricted to be mode, respectively.
providing 
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