P.penalty: Penalty matrix for higher order differences
Description
This function computes the matrix that penalizes the higher order
differences.
Usage
P.penalty(tt, P = c(0, 0, 1))
Arguments
tt
vector of the n discretization points or argvals.
P
vector of coefficients with the order of the differences. Default
value P=c(0,0,1) penalizes the second order difference.
Value
penalty matrix of size sum(n) x sum(n)
Details
For example, if P=c(0,1,2), the function return the penalty matrix
the second order difference of a vector \(tt\). That is $$v^T P_j tt=
\sum_{i=3} ^{n} (\Delta tt_i) ^2$$ where $$\Delta tt_i= tt_i -2 tt_{i-1}
+ tt_{i-2}$$ is the second order difference. More details can be found in
Kraemer, Boulesteix, and Tutz (2008).
References
N. Kraemer, A.-L. Boulsteix, and G. Tutz (2008). Penalized
Partial Least Squares with Applications to B-Spline Transformations and
Functional Data. Chemometrics and Intelligent Laboratory Systems, 94, 60 -
69. http://dx.doi.org/10.1016/j.chemolab.2008.06.009