fda.usc (version 1.1.0)

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 $$v^T{P}_{j}tt=\sum _{i=3}^n(\mathrm{\Delta }t{t}_i{)}^2$$ where $$\mathrm{\Delta }t{t}_i=t{t}_i-2t{t}_{i-1}+t{t}_{i-2}$$ 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

See Also

fdata2ppls

Examples

P.penalty((1:10)/10,P=c(0,0,1))
# a more detailed example can be found under script file }
<keyword>math</keyword>