evaluateLogConDens {logcondens}R Documentation

Evaluates the Log-Density Estimator at an Arbitrary Real Number x0

Description

Based on the output of the function activeSetLogCon, this gives the values of the functions

widehat varphi_m(t)

widehat f_m(t) = exp(widehat varphi_m(t))

widehat F_m(t) = int_{x_1}^t exp(widehat varphi_m(t)) dt

at an arbitrary real number t = x_0. The exact formula for widehat F_m and t in [x_j,x_{j+1}] is

widehat F_m(t) = widehat F_m(x_j) + (x_{j+1}-x_j) JBig(widehat varphi_j, widehat varphi_{j+1}, frac{t-x_j}{x_{j+1}-x_j} Big)

for the function J introduced in Jfunctions.

Usage

evaluateLogConDens(x0, x, phi, Fhat, IsKnot)

Arguments

x0 Real number where the functions should be evaluated at.
x Vector {x} = (x_1, ..., x_m) of original observations (sorted).
phi Vector (widehat varphi_m(x_i))_{i=1}^m, as computed by activeSetLogCon.
Fhat Vector (widehat F_m(x_i))_{i=1}^m, as computed by activeSetLogCon.
IsKnot 0-1 vector giving the kinks of widehat varphi_m, as computed by activeSetLogCon.

Value

Vector (widehat varphi_m(x_0), widehat f_m(x_0), widehat F_m(x_0)).

Author(s)

Kaspar Rufibach, kaspar.rufibach@gmail.com

Lutz Duembgen, duembgen@stat.unibe.ch,
http://www.staff.unibe.ch/duembgen

See Also

This function uses the output of activeSetLogCon.

For log-concave density estimation via an iterative convex minorant algorithm see icmaLogCon.

Examples

## estimate gamma density
set.seed(1977)
x <- sort(rgamma(200, 2, 1))
res <- activeSetLogCon(x, w = NA, print = FALSE)

## compute function values at an arbitrary point
x0 <- (x[100] + x[101]) / 2
evaluateLogConDens(x0, x, res$phi, res$Fhat, res$IsKnot)

[Package logcondens version 1.3.3 Index]