Bootstrap samples of a functional statistic
provides bootstrap samples for functional data.
fdata.bootstrap( fdataobj, statistic = func.mean, alpha = 0.05, nb = 200, smo = 0, draw = FALSE, draw.control = NULL, ... )
fdataobj |
|
statistic |
Sample statistic. It must be a function that returns an
object of class |
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 |
draw.control |
List that it specifies the |
... |
Further arguments passed to or from other methods. |
The fdata.bootstrap() computes a confidence ball using bootstrap in
the following way:
Let X_1(t),...,X_n(t) the original data and T=T(X_1(t),...,X_n(t)) the sample' statistic.
Calculate the nb bootstrap resamples
(X*_1(t),...,X*_n(t)),
using the following scheme X*_i(t)=X_i(t)+Z(t)
where Z(t) is normally distributed with mean 0 and covariance matrix
γΣ_x, where Σ_x is the
covariance matrix of' (X*_1(t),...,X*_n(t))
and γ is the smoothing parameter.
Let T^{*j}=T(X^{*j}_1(t),...,X^{*j}_n(t)) the estimate using the j resample.
Compute d(T,T^{*j}), j=1,…,nb. Define the bootstrap confidence ball of level 1-α as CB(α)=X \in E such that d(T,X)<= dα being dα the quantile (1-α) 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-α as those resamples that fulfill the condition of
belonging to CB(α). The statistic used by
default is the mean (func.mean) but also other depth-based
functions can be used (see help(Descriptive)).
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.
Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@usc.es
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. http://www.jstatsoft.org/v51/i04/
See Also as Descriptive
## 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)
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