KernelChars {locpol}R Documentation

Kernel characteristics

Description

For a given kernel returns some of the most commonly used numeric values for functionals related to them.

Usage

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

Arguments

K A kernel as given in Kernels

Details

These functions returns some of the most commonly used numeric values related to the kernels. They are implemented as an attribute of every kernel. For the computations of the numeric value for these quantities, see references.

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.

normal-bracket38bracket-normal These functions are implemented via kernel attributes.

Author(s)

Jorge Luis Ojeda Cabrera.

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))

[Package locpol version 0.2-0 Index]