# optim.np: Smoothing of functional data using nonparametric kernel... In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

 optim.np R Documentation

## Smoothing of functional data using nonparametric kernel estimation

### Description

Smoothing of functional data using nonparametric kernel estimation with cross-validation (CV) or generalized cross-validation (GCV) methods.

### Usage

```optim.np(
fdataobj,
h = NULL,
W = NULL,
Ker = Ker.norm,
type.CV = GCV.S,
type.S = S.NW,
par.CV = list(trim = 0, draw = FALSE),
par.S = list(),
correl = TRUE,
verbose = FALSE,
...
)
```

### Arguments

 `fdataobj` `fdata` class object. `h` Smoothing parameter or bandwidth. `W` Matrix of weights. `Ker` Type of kernel used, by default normal kernel. `type.CV` Type of cross-validation. By default generalized cross-validation (GCV) method. Possible values are GCV.S and CV.S `type.S` Type of smothing matrix `S`. By default `S` is calculated by Nadaraya-Watson kernel estimator (`S.NW`). Possible values are `S.KNN`, `S.LLR`, `S.LPR` and `S.LCR`. `par.CV` List of parameters for type.CV: `trim`, the alpha of the trimming and `draw=TRUE` `par.S` List of parameters for `type.S`: `tt` for argvals, `h` for bandwidth, `Ker` for kernel, etc. `correl` logical. If `TRUE` the bandwidth parameter `h` is computed following the procedure described for De Brabanter et al. (2018). (option avalaible since v1.6.0 version) `verbose` If `TRUE` information about GCV values and input parameters is printed. Default is `FALSE`. `...` Further arguments passed to or from other methods. Arguments to be passed for kernel method.

### Details

Calculate the minimum GCV for a vector of values of the smoothing parameter `h`. Nonparametric smoothing is performed by the kernel function. The type of kernel to use with the parameter `Ker` and the type of smothing matrix `S` to use with the parameter `type.S` can be selected by the user, see function `Kernel`. W is the matrix of weights of the discretization points.

### Value

Returns GCV or CV values calculated for input parameters.

• `gcv` GCV or CV for a vector of values of the smoothing parameter `h`

• `fdataobj` `fdata` class object.

• `fdata.est` Estimated `fdata` class object.

• `h.opt` `h` value that minimizes CV or GCV method.

• `S.opt` Smoothing matrix for the minimum CV or GCV method.

• `gcv.opt` Minimum of CV or GCV method.

• `h` Smoothing parameter or bandwidth.

### Note

min.np deprecated.

### 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.

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

Hardle, W. Applied Nonparametric Regression. Cambridge University Press, 1994.

De Brabanter, K., Cao, F., Gijbels, I., Opsomer, J. (2018). Local polynomial regression with correlated errors in random design and unknown correlation structure. Biometrika, 105(3), 681-69.

Febrero-Bande, M., Oviedo de la Fuente, M. (2012). Statistical Computing in Functional Data Analysis: The R Package fda.usc. Journal of Statistical Software, 51(4), 1-28. https://www.jstatsoft.org/v51/i04/

Alternative method: `optim.basis`

### Examples

```## Not run:
# Exemple, phoneme DATA
data(phoneme)
mlearn<-phoneme\$learn[1:100]

out1<-optim.np(mlearn,type.CV=CV.S,type.S=S.NW)
np<-ncol(mlearn)
# variance calculations
y<-mlearn
out<-out1
i<-1
z=qnorm(0.025/np)
fdata.est<-out\$fdata.est
tt<-y[["argvals"]]
var.e<-Var.e(y,out\$S.opt)
var.y<-Var.y(y,out\$S.opt)
var.y2<-Var.y(y,out\$S.opt,var.e)

# plot estimated fdata and point confidence interval
upper.var.e<-fdata.est[i,]-z*sqrt(diag(var.e))
lower.var.e<-fdata.est[i,]+z*sqrt(diag(var.e))
dev.new()
plot(y[i,],lwd=1,
ylim=c(min(lower.var.e\$data),max(upper.var.e\$data)),xlab="t")
lines(fdata.est[i,],col=gray(.1),lwd=1)
lines(fdata.est[i,]+z*sqrt(diag(var.y)),col=gray(0.7),lwd=2)
lines(fdata.est[i,]-z*sqrt(diag(var.y)),col=gray(0.7),lwd=2)
lines(upper.var.e,col=gray(.3),lwd=2,lty=2)
lines(lower.var.e,col=gray(.3),lwd=2,lty=2)
legend("bottom",legend=c("Var.y","Var.error"),
col = c(gray(0.7),gray(0.3)),lty=c(1,2))

## End(Not run)

```

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