fda.usc (version 1.1.0)

fregre.bootstrap: 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

=TRUE, wild bootstrap. =FALSE, smoothed bootstrap.

type.wild

Type of distribution of V in wild bootstrap procedure, see rwild.

smo

(only for smoothed bootstrap) Smoothing parameter as a proportion of response variance.

smoX

(only for smoothed bootstrap) Smoothing parameter for fdata object as a proportion of variance-covariance matrix of the explanatory functional variable.

newX

(optional, only for smoothed bootstrap), new functional explanatory data of fdata class .

alpha

Significance level.

kmax.fix

=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.

Value

• Return:
• beta.boot
  Functional beta estimated by bootstrap method.
• norm.boot
  norm of diferences beetween the nboot betas estimated by bootstrap and beta estimated by regression model.
• coefs.boot
  nboot X nbasis of bootstrap estimated coefficients of basis
• knn.fix
  nb basis, CP or PLS factors selected in each regression.
• y.pred
  nboot X n matrix of predicted response values.
• y.boot
  nboot X n matrix of bootstrap predicted response values.

Details

Compute the beta estimated in influence.fdata for functional regression 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).

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. http://www.jstatsoft.org/v51/i04/

See Also

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

Examples

data(tecator)
x=tecator$absorp.fdata[1:129]
y=tecator$y$Fat[1:129]
nb<-100
## Time-consuming
# res.pc=fregre.pc(x,y,1:6)
# res.boot1=fregre.bootstrap(res.pc,nb=nb,wild=FALSE,kmax.fix=TRUE)

## predicted responses by bootstrap  with FPC and FPLS basis
# newx=tecator$absorp.fdata[-c(1:129)]
# newy=tecator$y$Fat[-c(1:129)]
# res.pls=fregre.pls(x,y)
# res.boot2=fregre.bootstrap(res.pls,nb=nb,wild=FALSE,newX=newx,kmax.fix=TRUE)
# res.boot3=fregre.bootstrap(res.pc,nb=nb,wild=FALSE,newX=newx,kmax.fix=TRUE)