Local_LL_all {logcondens}R Documentation

Log-likelihood, New Candidate and Directional Derivative for L

Description

Computes the value of the log-likelihood function

L(varphi) = sum_{i=1}^m w_i varphi(x_i) - int_{x_1}^{x_m} exp(varphi(t)) dt,

a new candidate for varphi via the Newton method as well as the directional derivative of {varphi} to L({varphi}) into that direction.

Usage

Local_LL_all(x, w, phi)

Arguments

x Vector of independent and identically distributed numbers, with strictly increasing entries.
w Optional vector of nonnegative weights corresponding to {x}, where w_1 > 0 and w_m > 0. These raw weights are normalized in order to sum to one. Default: w_i = 1/m.
phi Some vector {varphi} of the same length as {x} and {w}.

Value

ll Value L(varphi) of the log-likelihood function at varphi.
phi_new New candidate for varphi via the Newton-method, using the complete Hessian matrix.
dirderiv Directional derivative of varphi to L(varphi) into the direction varphi_{new}.

Author(s)

Kaspar Rufibach, kaspar.rufibach@gmail.com

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


[Package logcondens version 1.3.3 Index]