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 η\eta of a quadratic approximation to the reparametrized original log-likelihood function

L(ϕ)=i=1mwiϕ(xi)exp(ϕ(t))dt.L(\phi) = \sum_{i=1}^m w_i \phi(x_i) - \int_{-\infty}^{\infty} \exp(\phi(t)) dt.

where LL is parametrized via

η(ϕ)=(ϕ1,(η1+j=2i(xixi1)ηi)i=2m).{\bold{\eta}}({\bold{\phi}}) = \Bigl(\phi_1, \Bigl(\eta_1+ \sum_{j=2}^i (x_i-x_{i-1})\eta_i\Bigr)_{i=2}^m\Bigr).

ϕ{\bold{\phi}}: vector (ϕ(xi))i=1m(\phi(x_i))_{i=1}^m representing concave, piecewise linear function ϕ\phi,
η{\bold{\eta}}: vector representing successive slopes of ϕ.\phi.

Usage

quadDeriv(dx, w, eta)

Arguments

dx

Vector (0,xixi1)i=2m.(0, x_i-x_{i-1})_{i=2}^m.

w

Vector of weights as in activeSetLogCon.

eta

Vector η.{\bold{\eta}}.

Value

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

Note

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

Author(s)

Kaspar Rufibach, kaspar.rufibach@gmail.com,
http://www.kasparrufibach.ch

Lutz Duembgen, duembgen@stat.unibe.ch,
https://www.imsv.unibe.ch/about_us/staff/prof_dr_duembgen_lutz/index_eng.html

See Also

quadDeriv is used by the function icmaLogCon.


[Package logcondens version 2.1.8 Index]