locpol (version 0.8.0)

equivKernel: Equivalent Kernel.

Description

Computes the Equivalent kernel for the local polynomial estimation.

Usage

equivKernel(kernel,nu,deg,lower=dom(kernel)[[1]],upper=dom(kernel)[[2]],
	subdivisions=25)

Value

Returns a vector whose components are the equivalent kernel used to compute the local polynomial estimator for the derivatives in nu.

Arguments

nu

Orders of derivative to estimate.

deg

Degree of Local polynomial estimator.

kernel

Kernel used to perform the estimation, see Kernels

lower, upper

Integration limits.

subdivisions

the maximum number of subintervals.

Author

Jorge Luis Ojeda Cabrera.

Details

The definition of the Equivalent kernel for the local polynomial estimation can be found in page 64 in Fan and Gijbels(1996). The implementation uses computeMu to compute matrix \(S\) and then returns a function object

References

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

See Also

cteNuK, adjNuK.

Examples

##	Some kernels and equiv. for higher order
##	compare with p=1
curve(EpaK(x),-3,3,ylim=c(-.5,1))
f <- equivKernel(EpaK,0,3)
curve(f(x),-3,3,add=TRUE,col="blue")
curve(gaussK(x),-3,3,add=TRUE)
f <- equivKernel(gaussK,0,3)
curve(f(x),-3,3,add=TRUE,col="blue")
##	Draw several Equivalent locl polynomial kernels
curve(EpaK(x),-3,3,ylim=c(-.5,1))
for(p in 1:5){
	curve(equivKernel(gaussK,0,p)(x),-3,3,add=TRUE)
    }