# Kernel: Symmetric Smoothing Kernels. In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

 Kernel R Documentation

## Symmetric Smoothing Kernels.

### Description

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

### Usage

```Kernel(u, type.Ker = "Ker.norm")
```

### Arguments

 `u` Data. `type.Ker` Type of Kernel. By default normal kernel.

### Details

 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` Cosine Kernel: `Ker.cos` Epanechnikov Kernel: `Ker.epa` Triweight Kernel: `Ker.tri` Quartic Kernel: `Ker.quar` Uniform Kernel: `Ker.unif`

### Value

Returns symmetric kernel.

### Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@udc.es

### 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)
```

fda.usc documentation built on Oct. 17, 2022, 9:06 a.m.