# fregre.bootstrap: Bootstrap regression In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

 fregre.bootstrap R Documentation

## Bootstrap regression

### Description

Estimate the beta parameter by wild or smoothed bootstrap procedure

### Usage

```fregre.bootstrap(
model,
nb = 500,
wild = TRUE,
type.wild = "golden",
newX = NULL,
smo = 0.1,
smoX = 0.05,
alpha = 0.95,
kmax.fix = FALSE,
draw = TRUE,
...
)
```

### Arguments

 `model` `fregre.pc`, `fregre.pls` or `fregre.basis` object. `nb` Number of bootstrap samples. `wild` Naive or smoothed bootstrap depending of the `smo` and `smoX` parameters. `type.wild` Type of distribution of V in wild bootstrap procedure, see `rwild`. `newX` A `fdata` class containing the values of the model covariates at which predictions are required (only for smoothed bootstrap). `smo` If >0, smoothed bootstrap on the residuals (proportion of response variance). `smoX` If >0, smoothed bootstrap on the explanatory functional variable `fdata` (proportion of variance-covariance matrix of `fdata` object. `alpha` Significance level used for graphical option, `draw=TRUE`. `kmax.fix` The number of maximum components to consider in each bootstrap iteration. =TRUE, the bootstrap procedure considers the same number of components used in the previous fitted model. =FALSE, the bootstrap procedure estimates the best components in each iteration. `draw` =TRUE, plot the bootstrap estimated beta, and (optional) the CI for the predicted response values. `...` Further arguments passed to or from other methods.

### Details

Estimate the beta parameter by wild or smoothed bootstrap procedure using principal components representation `fregre.pc`, Partial least squares components (PLS) representation `fregre.pls` or basis representation `fregre.basis`.
If a new curves are in `newX` argument the bootstrap method estimates the response using the bootstrap resamples.

If the model exhibits heteroskedasticity, the use of wild bootstrap procedure is recommended (by default).

### Value

Return:

• `model` `fregre.pc`, `fregre.pls` or `fregre.basis` object.

• `beta.boot` functional beta estimated by the `nb` bootstrap regressions.

• `norm.boot` norm of diferences beetween the nboot betas estimated by bootstrap and beta estimated by regression model.

• `coefs.boot` matrix with the bootstrap estimated basis coefficients.

• `kn.boot` vector or list of length `nb` with index of the basis, PC or PLS factors selected in each bootstrap regression.

• `y.pred` predicted response values using `newX` covariates.

• `y.boot` matrix of bootstrap predicted response values using `newX` covariates.

• `newX` a `fdata` class containing the values of the model covariates at which predictions are required (only for smoothed bootstrap).

### Author(s)

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

### References

Febrero-Bande, M., Galeano, P. and Gonzalez-Manteiga, W. (2010). Measures of influence for the functional linear model with scalar response. Journal of Multivariate Analysis 101, 327-339.

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/

See Also as: `fregre.pc`, `fregre.pls`, `fregre.basis`, .

### Examples

```## Not run:
data(tecator)
iest<-1:165
x=tecator\$absorp.fdata[iest]
y=tecator\$y\$Fat[iest]
nb<-25  ## Time-consuming
res.pc=fregre.pc(x,y,1:6)
# Fix the compontents used in the each regression
res.boot1=fregre.bootstrap(res.pc,nb=nb,wild=FALSE,kmax.fix=TRUE)
# Select the "best" compontents used in the each regression
res.boot2=fregre.bootstrap(res.pc,nb=nb,wild=FALSE,kmax.fix=FALSE)
res.boot3=fregre.bootstrap(res.pc,nb=nb,wild=FALSE,kmax.fix=10)
## predicted responses and bootstrap confidence interval
newx=tecator\$absorp.fdata[-iest]
res.boot4=fregre.bootstrap(res.pc,nb=nb,wild=FALSE,newX=newx,draw=TRUE)

## End(Not run)
```

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