# D.m: Calculating the penalty matrix In pendensity: Density Estimation with a Penalized Mixture Approach

## 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

 1 D.m(penden.env) 

## Arguments

 penden.env Containing all information, environment of pendensity()

## 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.

## Value

Returning the penalty matrix.

## Author(s)

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

## 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 2, 2019, 3:58 a.m.