Derv2: Calculating the second order derivative with and without penalty.
Description
Calculating the second order derivative of the likelihood function of
the pencopula approach w.r.t. the parameter b. Thereby, for later use,
the program calculates the second order derivative with and without the
penalty. Moreover, Derv2 seperates the calculation for temporary weights
b in iteration and final weights b.
Usage
Derv2(penden.env, temp = FALSE)
Arguments
penden.env
Containing all information, environment of pendensity()
temp
smoothing parameter lambda
Value
Derv2.pensecond order derivative w.r.t. beta with penalty
Derv2.calsecond order derivative w.r.t. beta without
penalty. Needed for calculating of e.g. AIC.
Derv2.cal and Derv2.pen are saved in the environment.
Details
We approximate the second order derivative in this approach with the negative fisher information.
References
Flexible Copula Density Estimation with Penalized
Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2011), to appear.