fda.usc (version 2.0.2)

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 manuel.oviedo@usc.es

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

Run this code
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)

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