fda.usc (version 1.2.3)

Kernel.asymmetric: Asymmetric Smoothing Kernel

Description

Represent Asymmetric Smoothing Kernels: normal, cosine, triweight, quartic and uniform.

AKer.norm=ifelse(u>=0,2*dnorm(u),0)

AKer.cos=ifelse(u>=0,pi/2*(cos(pi*u/2)),0)

AKer.epa=ifelse(u>=0 & u<=1,3 2*(1-u^2),0)<="" td="">

AKer.tri=ifelse(u>=0 & u<=1,35 16*(1-u^2)^3,0)<="" td="">

AKer.quar=ifelse(u>=0 & u<=1,15 8*(1-u^2)^2,0)<="" td="">

AKer.unif=ifelse(u>=0 & u<=1,1,0)< td="">

Usage

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

Arguments

type.Ker

Type of asymmetric metric kernel, by default asymmetric normal kernel.

u

Data.

Value

res

Returns asymmetric kernel.

Details

Type of Asymmetric kernel:

Asymmetric Normal Kernel: AKer.norm

Asymmetric Cosine Kernel: AKer.cos

Asymmetric Epanechnikov Kernel: AKer.epa

Asymmetric Triweight Kernel: AKer.tri

Asymmetric Quartic Kernel: AKer.quar

Asymmetric Uniform Kernel: AKer.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.asymmetric(u=y)
b<-Kernel.asymmetric(type.Ker="AKer.tri",u=y)
c=AKer.cos(y)