fdata.bootstrap: Bootstrap samples of a functional statistic

In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

Bootstrap samples of a functional statistic

Description

provides bootstrap samples for functional data.

Usage

fdata.bootstrap(
  fdataobj,
  statistic = func.mean,
  alpha = 0.05,
  nb = 200,
  smo = 0,
  draw = FALSE,
  draw.control = NULL,
  ...
)

Arguments

fdataobj	fdata class object.
statistic	Sample statistic. It must be a function that returns an object of class fdata. By default, it uses sample mean func.mean. See Descriptive for other statistics.
alpha	Significance value.
nb	Number of bootstrap resamples.
smo	The smoothing parameter for the bootstrap samples as a proportion of the sample variance matrix.
draw	If TRUE, plot the bootstrap samples and the statistic.
draw.control	List that it specifies the col, lty and lwd for objects: fdataobj, statistic, IN and OUT.
...	Further arguments passed to or from other methods.

Details

The fdata.bootstrap computes a confidence ball using bootstrap in the following way:

• Let X_1(t),\ldots,X_n(t) be the original data and T=T(X_1(t),\ldots,X_n(t)) be the sample statistic.

• Calculate the nb bootstrap resamples \left\{X_{1}^{*}(t),\cdots,X_n^*(t)\right\}, using the following scheme: X_i^*(t)=X_i(t)+Z(t), where Z(t) is normally distributed with mean 0 and covariance matrix \gamma\Sigma_x, where \Sigma_x is the covariance matrix of \left\{X_1(t),\ldots,X_n(t)\right\} and \gamma is the smoothing parameter.

• Let T^{*j}=T(X^{*j}_1(t),...,X^{*j}_n(t)) be the estimate using the j resample.

• Compute d(T,T^{*j}), j=1,\ldots,nb. Define the bootstrap confidence ball of level 1-\alpha as CB(\alpha)=X\in E such that d(T,X)\leq d_{\alpha} being d_{\alpha} the quantile (1-\alpha) of the distances between the bootstrap resamples and the sample estimate.

The fdata.bootstrap function allows us to define a statistic calculated on the nb resamples, control the degree of smoothing by smo argument and represent the confidence ball with level 1-\alpha as those resamples that fulfill the condition of belonging to CB(\alpha). The statistic used by default is the mean (func.mean) but also other depth-based functions can be used (see help(Descriptive)).

Value

• statistic: fdata class object with the statistic estimate from nb bootstrap samples.

• dband: Bootstrap estimate of (1-alpha)% distance.

• rep.dist: Distance from every replicate.

• resamples: fdata class object with the bootstrap resamples.

• fdataobj: fdata class object.

Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente [e-mail]

References

Cuevas A., Febrero-Bande, M. and Fraiman, R. (2007). Robust estimation and classification for functional data via projection-based depth notions. Computational Statistics 22, 3: 481-496.

Cuevas A., Febrero-Bande, M., Fraiman R. 2006. On the use of bootstrap for estimating functions with functional data. Computational Statistics and Data Analysis 51: 1063-1074.

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

See Also as Descriptive

Examples

## Not run: 
data(tecator)
absorp<-tecator$absorp.fdata
# Time consuming
#Bootstrap for Trimmed Mean with depth mode
out.boot=fdata.bootstrap(absorp,statistic=func.trim.FM,nb=200,draw=TRUE)
names(out.boot)
#Bootstrap for Median with with depth mode
control=list("col"=c("grey","blue","cyan"),"lty"=c(2,1,1),"lwd"=c(1,3,1))
out.boot=fdata.bootstrap(absorp,statistic=func.med.mode,
draw=TRUE,draw.control=control)

## End(Not run)

fda.usc documentation built on April 4, 2025, 4:35 a.m.