Derv2 {pendensity}R Documentation

Calculating the second order derivative with and without penalty

Description

Calculating the second order derivative of the likelihood function of the pendensity approach w.r.t. the parameter beta. Thereby, for later use, the program returns the second order derivative with and without the penalty.

Usage

Derv2(penden.env, lambda0)

Arguments

penden.env Containing all information, environment of pendensity()
lambda0 smoothing parameter lambda

Details

We approximate the second order derivative in this approach with the negative fisher information.

J(beta)= partial^2 l(beta) / (partial(beta) partial(beta)) = sum(s[i](beta) s[i]^T(beta))

Therefore we construct the second order derivative of the i-th observation w.r.t. beta with the outer product of the matrix Derv1.cal and the i-th row of the matrix Derv1.cal.
The penalty is computed as

lambda Dm

.

Value

Derv2.pen second order derivative w.r.t. beta with penalty
Derv2.cal second order derivative w.r.t. beta without penalty. Needed for calculating of e.g. AIC.

Author(s)

Christian Schellhase <cschellhase@wiwi.uni-bielefeld.de>

References

Density Estimation with a Penalized Mixture Approach, Kauermann G. and Schellhase C. (2009), to appear.


[Package pendensity version 0.2 Index]