# S.np: Smoothing matrix by nonparametric methods In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

## Description

Provides the smoothing matrix `S` for the discretization points `tt`

## Usage

 ```1 2 3 4 5 6 7 8 9``` ```S.LLR(tt, h, Ker = Ker.norm, w = NULL, cv = FALSE) S.LPR(tt, h, p = 1, Ker = Ker.norm, w = NULL, cv = FALSE) S.LCR(tt, h, Ker = Ker.norm, w = NULL, cv = FALSE) S.NW(tt, h = NULL, Ker = Ker.norm, w = NULL, cv = FALSE) S.KNN(tt, h = NULL, Ker = Ker.unif, w = NULL, cv = FALSE) ```

## Arguments

 `tt` Vector of discretization points or distance matrix `mdist` `h` Smoothing parameter or bandwidth. In S.KNN, number of k-nearest neighbors. `Ker` Type of kernel used, by default normal kernel. `w` Optional case weights. `cv` If `TRUE`, cross-validation is done. `p` Polynomial degree. be passed by default to create.basis

## Details

Options:

• Nadaraya-Watson kernel estimator (S.NW) with bandwidth parameter `h`.

• Local Linear Smoothing (S.LLR) with bandwidth parameter `h`.

• K nearest neighbors estimator (S.KNN) with parameter `knn`.

• Polynomial Local Regression Estimator (S.LCR) with parameter of polynomial `p` and of kernel `Ker`.

• Local Cubic Regression Estimator (S.LPR) with kernel `Ker`.

## Value

Return the smoothing matrix `S`.

• `S.LLR` return the smoothing matrix by Local Linear Smoothing.

• `S.NW` return the smoothing matrix by Nadaraya-Watson kernel estimator.

• `S.KNN` return the smoothing matrix by k nearest neighbors estimator.

• `S.LPR` return the smoothing matrix by Local Polynomial Regression Estimator.

• `S.LCR` return the smoothing matrix by Cubic Polynomial Regression.

## Author(s)

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

## References

Ferraty, F. and Vieu, P. (2006). Nonparametric functional data analysis. Springer Series in Statistics, New York.

Wasserman, L. All of Nonparametric Statistics. Springer Texts in Statistics, 2006.

Opsomer, J. D., and Ruppert, D. (1997). Fitting a bivariate additive model by local polynomial regression. The Annals of Statistics, 25(1), 186-211.

See Also as `S.basis`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```## Not run: tt=1:101 S=S.LLR(tt,h=5) S2=S.LLR(tt,h=10,Ker=Ker.tri) S3=S.NW(tt,h=10,Ker=Ker.tri) S4=S.KNN(tt,h=5,Ker=Ker.tri) par(mfrow=c(2,3)) image(S) image(S2) image(S3) image(S4) S5=S.LPR(tt,h=10,p=1, Ker=Ker.tri) S6=S.LCR(tt,h=10,Ker=Ker.tri) image(S5) image(S6) ## End(Not run) ```