CVThresh (version 1.1.2)

ppoly: Piecewise polynomial function

Description

This function generates Piecewise polynomial function values for \(n\) equally spaced points in \([0,1]\).

Usage

ppoly(norx=1024)

Arguments

norx

the number of data or x values in [0, 1]

Value

Piecewise polynomial function values \(f(\frac{i}{n}), i=1,\ldots,n\) and its variability \(||f|| = \frac{\sum_{i=1}^n (f_i - \bar f)^2}{n-1}\) where \(\bar f = \frac{\sum_{i=1}^n f_i}{n}\).

Details

Piecewise polynomial function with the discontinuity is introduced by Nason and Silverman (1994) and is useful test function evaluating a wavelet shrinkage method.

References

Nason, G.P. and Silverman, B.W. (1994) The discrete wavelet transform in S. Journal of Computational and Graphical Statistics, 3, 163--191.

See Also

dopp, heav, fg1.

Examples

# NOT RUN {
testpoly <- ppoly(1024)
plot(testpoly$x, testpoly$meanf, xlab="", ylab="", 
     main="Plot of Piecewise polynomial function", type="l")
# }