fda.usc (version 2.1.0)

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)
	AKer.tri=ifelse(u>=0 & u<=1,35/16*(1-u^2)^3,0)
	AKer.quar=ifelse(u>=0 & u<=1,15/8*(1-u^2)^2,0)
	AKer.unif=ifelse(u>=0 & u<=1,1,0)

Usage

Kernel.asymmetric(u, type.Ker = "AKer.norm")

Value

Returns asymmetric kernel.

Arguments

u

Data.

type.Ker

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

Author

Manuel Febrero-Bande, Manuel Oviedo de la Fuente

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)