Local_LL_all {logcondens}

Log-likelihood, New Candidate and Directional Derivative for L

Description

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.

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 {\bold{x}_m}.

phi

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

Value

ll

Value L(\phi) of the log-likelihood function at \phi.

phi_new

New candidate for \phi via the Newton-method, using the complete Hessian matrix.

dirderiv

Directional derivative of \phi \to L(\phi) into the direction \phi_{new}.

Note

This function is not intended to be invoked by the end user.

Author(s)

Kaspar Rufibach, [e-mail],
http://www.kasparrufibach.ch

Lutz Duembgen, [e-mail],
https://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html