dlcd {LogConcDEAD}R Documentation

Evaluation of a log-concave maximum likelihood estimator at a point

Description

This function evaluates the density function of a log-concave maximum likelihood estimator at a point or points.

Usage

dlcd(x,lcd, uselog=FALSE) 
lcd.eval(lcd, po, uselog=FALSE) 

Arguments

x, po Point (or matrix of points) at which the maximum likelihood estimator should be evaluated
lcd Object of class "LogConcDEAD" (typically output from mlelcd)
uselog Scalar logical: should the estimator should be calculated on the log scale?

Details

A log-concave maximum likelihood estimate f_n is satisfies log f_n = h_y for some y in R^n, where

h_y(x) = inf{h(x): h concave, h(x_i) >= y_i for i = 1, ..., n}.

Functions of this form may equivalently be specified by dividing C_n, the convex hull of the data into simplices C_j for j in J (triangles in 2d, tetrahedra in 3d etc), and setting

f(x) = exp{b_j^T x - beta_j}

for x in C_j, and f(x) = 0 for x not in C_n. The estimated density is zero outside the convex hull of the data.

The estimate may therefore be evaluated by finding the appropriate simplex C_j, then evaluating f(x) = exp{b_j^T x - beta_j} (if x not in C_n, set f(x) = 0).

For examples, see mlelcd.

lcd.eval is deprecated, but retained for compatibility with previous versions.

Value

A vector of maximum likelihood estimate (or log maximum likelihood estimate) values, as evaluated at the points x.

Author(s)

Madeleine Cule mlc40@cam.ac.uk

Robert Gramacy

Richard Samworth

See Also

mlelcd


[Package LogConcDEAD version 1.3-3 Index]