# P.penalty

0th

Percentile

##### Penalty matrix for higher order differences

This function computes the matrix that penalizes the higher order differences.

Keywords
math
##### 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.

##### 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).

##### Value

penalty matrix of size sum(n) x sum(n)

##### Note

The discretization points can be equidistant or not.

##### 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

fdata2pls

• P.penalty
##### Examples
# NOT RUN {
P.penalty((1:10)/10,P=c(0,0,1))
# a more detailed example can be found under script file
# }

Documentation reproduced from package fda.usc, version 2.0.1, License: GPL-2

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