Symmetric Smoothing Kernels.
Represent symmetric smoothing kernels:: normal, cosine, triweight, quartic and uniform.
Kernel(u, type.Ker = "Ker.norm")
u |
Data. |
type.Ker |
Type of Kernel. By default normal kernel. |
| Ker.norm=dnorm(u) | |
| Ker.cos=ifelse(abs(u)<=1,pi/4*(cos(pi*u/2)),0) | |
| Ker.epa=ifelse(abs(u)<=1,3/4*(1-u^2),0) | |
| Ker.tri=ifelse(abs(u)<=1,35/32*(1-u^2)^3,0) | |
| Ker.quar=ifelse(abs(u)<=1,15/16*(1-u^2)^2,0) | |
| Ker.unif=ifelse(abs(u)<=1,1/2,0) | |
Type of kernel:
Normal Kernel: Ker.norm
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Cosine Kernel: Ker.cos
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Epanechnikov Kernel: Ker.epa
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Triweight Kernel: Ker.tri
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Quartic Kernel:
Ker.quar
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Uniform Kernel: Ker.unif
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Returns symmetric kernel.
Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@usc.es
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.
y=qnorm(seq(.1,.9,len=100)) a<-Kernel(u=y) b<-Kernel(type.Ker="Ker.tri",u=y) c=Ker.cos(y)
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