Derv2: Calculating the second order derivative with and without...

Description Usage Arguments Details Value Author(s) References

View source: R/Derv2.R

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

1
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.

\eqn{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

\eqn{ 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 <[email protected]>

References

Density Estimation with a Penalized Mixture Approach, Schellhase C. and Kauermann G. (2012), Computational Statistics 27 (4), p. 757-777.


pendensity documentation built on May 29, 2017, 9:04 a.m.