fda.usc (version 1.2.3)

Kernel: Symmetric Smoothing Kernels.

Description

Represent symmetric smoothing kernels:: normal, cosine, triweight, quartic and uniform.

Ker.norm=dnorm(u)

Ker.cos=ifelse(abs(u)<=1,pi 4*(cos(pi*u="" 2)),0)<="" td="">

Ker.epa=ifelse(abs(u)<=1,3 4*(1-u^2),0)<="" td="">

Ker.tri=ifelse(abs(u)<=1,35 32*(1-u^2)^3,0)<="" td="">

Ker.quar=ifelse(abs(u)<=1,15 16*(1-u^2)^2,0)<="" td="">

Ker.unif=ifelse(abs(u)<=1,1 2,0)<="" td="">

Usage

Kernel(u,type.Ker="Ker.norm")
Ker.norm(u)
Ker.cos(u)
Ker.epa(u)
Ker.tri(u)
Ker.quar(u)
Ker.unif(u)

Arguments

type.Ker

Type of Kernel. By default normal kernel.

u

Data.

Value

res

Returns symmetric kernel.

Details

Type of kernel:

Normal Kernel: Ker.norm

Cosine Kernel: Ker.cos

Epanechnikov Kernel: Ker.epa

Triweight Kernel: Ker.tri

Quartic Kernel: Ker.quar

Uniform Kernel: Ker.unif

References

Ferraty, F. and Vieu, P. (2006). Nonparametric functional data analysis. Springer Series in Statistics, New York.

Hardle, W. Applied Nonparametric Regression. Cambridge University Press, 1994.

Examples

y=qnorm(seq(.1,.9,len=100))
a<-Kernel(u=y)
b<-Kernel(type.Ker="Ker.tri",u=y)
c=Ker.cos(y)