locpol (version 0.8.0)

KernelChars: Kernel characteristics

Description

For a given kernel these functions return some of the most commonly used numeric values related to them.

Usage

RK(K)
	RdK(K)
	mu2K(K)
	mu0K(K)
	K4(K)
	dom(K)

Value

A numeric value returning:

RK

The \(L_2\) norm of K.

RdK

The \(L_2\) norm of the derivative of K.

mu2K

The second order moment of K.

mu2K

The zeroth order moment of K.

dom

The support of K.

K4

The fourth order autoconvolution of K at \(x=0\).

Arguments

K

A kernel as given in Kernels

Author

Jorge Luis Ojeda Cabrera.

Details

Most of these functions are implemented as an attribute of every kernel. For the computations of the numeric value for these quantities, see references.

References

Fan, J. and Gijbels, I. Local polynomial modelling and its applications\/. Chapman & Hall, London (1996).

Wand, M.~P. and Jones, M.~C. Kernel smoothing\/. Chapman and Hall Ltd., London (1995).

See Also

Kernels, Compute kernel values.

Examples

	##	Note that lower and upper params are set in the definition to
	##	use 'dom()' function.
	g <- function(kernels)
	{
		mu0 <- sapply(kernels,function(x) computeMu0(x,))
		mu0.ok <- sapply(kernels,mu0K)
		mu2 <- sapply(kernels,function(x) computeMu(2,x))
		mu2.ok <- sapply(kernels,mu2K)
		Rk.ok <- sapply(kernels,RK)
		RK <- sapply(kernels,function(x) computeRK(x))
		K4 <- sapply(kernels,function(x) computeK4(x))
		res <- data.frame(mu0,mu0.ok,mu2,mu2.ok,RK,Rk.ok,K4)
		res
	}
	g(kernels=c(EpaK,gaussK,TriweigK,TrianK))