fg1 {CVThresh}

fg1 function

Description

This function generates fg1 function values for n equally spaced points in [0,1].

Usage

fg1(norx=1024)

Arguments

norx

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

Details

A smooth function fg1 is introduced by Fan and Gijbels (1995) and is useful test function evaluating a wavelet shrinkage method.

Value

fg1 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}.

References

Fan, J. and Gijbels, I. (1995) Data-driven bandwidth selection in local polynomial fitting: Variable bandwidth and spatial adaptation. Journal of the Royal Statistical Society Ser. B 57, 371–394.

See Also

dopp, heav, ppoly.

Examples

testfg1 <- fg1(1024)
plot(testfg1$x, testfg1$meanf, xlab="", ylab="", 
     main="Plot of fg1 function", type="l")