pendensity (version 0.2.5)

D.m: Calculating the penalty matrix

Description

calculating the penalty matrix depending on the number of covariates 'p', the order of differences to be penalized 'm', the corresponding difference matrix 'L' of order 'm', the covariate matrix 'Z', the number of observations 'n' and the number of knots 'K'.

Usage

D.m(penden.env)

Arguments

penden.env

Containing all information, environment of pendensity()

Value

• Returning the penalty matrix.

Details

The penalty matrix is calculated as

$D_m=(L^T \otimes I_p) (I_{K-m} \otimes \frac{Z^T Z}{n}) (L \otimes I_p)$

The needed values are saved in the environment.

References

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