quadDeriv {logcondens}R Documentation

Gradient and Diagonal of Hesse Matrix of Quadratic Approximation to Log-Likelihood Function L

Description

Computes gradient and diagonal of the Hesse matrix w.r.t. to eta of a quadratic approximation to the reparametrized original log-likelihood function

L(varphi) = sum_{i=1}^m w_i varphi(x_i) - int_{-infty}^{infty} exp(varphi(t)) dt.

where L is parametrized via

{eta}({varphi}) = Bigl(varphi_1, Bigl(eta_1+ sum_{j=2}^i (x_i-x_{i-1})eta_iBigr)_{i=2}^mBigr).

{varphi}: vector (varphi(x_i))_{i=1}^m representing concave, piecewise linear function varphi,
{eta}: vector representing successive slopes of varphi.

Usage

quadDeriv(dx, w, eta)

Arguments

dx Vector (0, x_i-x_{i-1})_{i=2}^m.
w Vector of weights as in activeSetLogCon.
eta Vector {eta}.

Value

m times 2 matrix. First column contains gradient and second column diagonal of Hesse matrix.

Author(s)

Kaspar Rufibach, kaspar.rufibach@gmail.com

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

See Also

quadDeriv is used by the function icmaLogCon.


[Package logcondens version 1.3.3 Index]