ILS (version 0.1.0)

bootstrap.quantile: Compute functional (FDA) Mandel's h and k statistics

Description

This function is used to compute functional (FDA)Mandel's h and k, statistics, required to perform Interlaboratory studies, and to detect non-consistent laboratories where data show a functional form (curve). In addition, bootstrap resampling methodology is used to estimate functional distributions. This allow to perform bootstrap confidence bands for FDA h and k statistics.

Usage

bootstrap.quantile(x, ...)
"bootstrap.quantile"(x, argvals = NULL, rangeval = NULL, statistic = c("h", "k"), method = c("Walter", "Depth"), alpha = 0.05, quantile = 0.9, ball = FALSE, nb = 200, smo = 0, draw = TRUE, draw.control = NULL, x.co = NULL, y.co = NULL, legend = TRUE, col = NULL, ...)
"bootstrap.quantile"(x, statistic = c("h", "k"), method = c("Walter", "Depth"), alpha = 0.05, quantile = 0.9, ball = FALSE, nb = 200, smo = 0, draw = TRUE, draw.control = NULL, x.co = NULL, y.co = NULL, legend = TRUE, col = NULL, ...)
"print"(x, ...)
"summary"(object, ...)

Arguments

x

A bootstrap.quantile object for which a print is desired.

...

Arguments passed to or from methods.

argvals

Argvals, by default: 1:p.

rangeval

Range of discretization points, by default: range(argvals).

statistic

Sample statistic used for the interlaboratory analysis. By default, it uses sample h.

method

Quantile method used to estimate the critical quantile of the h and k statistics.

alpha

Significance level.

quantile

Probability with value in [0,1]

ball

Logical argument. If draw = TRUE and ball = TRUE, i bootstrap curves and quantiles functions are plotted. They correspond to (1-alpha/2)*100 [%] most central bootstrap resampling curves of q quantile. If draw = TRUE and ball = FALSE, the functional quantile q [%] is determined.

nb

Number of bootstrap resamples.

smo

Smoothing parameter for the bootstrap resamples, defined as a proportion of the sample variance matrix.

draw

Default TRUE, it plots the bootstrap samples and the h or k statistic. It depends on the ball parameter.

draw.control

List that specifies the col, lty and lwd plot arguments for the objects lab.fqcs, statistic, IN and OUT.

x.co

It speficies the x co-ordinates to be used to place a legend.

y.co

It specifies the y co-ordinates to be used to place a legend.

legend

Logical argument. Default is TRUE then The legend default is used.

col

Color specifications

object

A bootstrap.quantile object for which a summary is desired.

References

Febrero-Bande, M. and Oviedo, M. (2012), "Statistical computing in functional data analysis: the R package fda.usc". Journal of Statistical Software 51 (4), 1-28.

Cuevas A., Febrero-Bande, M. and Fraiman, R. (2006), "On the use of the bootstrap for estimating functions with functional data". Computational Statistics & Data Analysis 51, 2, 1063-1074.

Naya, S., Tarrio-Saavedra. J., Lopez- Beceiro, J., Francisco Fernandez, M., Flores, M. and Artiaga, R. (2014), "Statistical functional approach for interlaboratory studies with thermal data". Journal of Thermal Analysis and Calorimetry, 118,1229-1243.

Lopez-Pintado, S. and Romo, J. (2009), "On the concept of depth for functional data", Journal of the American Statistical Association, 104, 486-503.

Walter, S. (2011), Defining Quantiles for Functional Data: with an Application to the Reversal of Stock Price Decreases, Department of Math. and Stat. The Uni. of Melbourne.

Examples

## Not run: 
# library(ILS)
# data(TG)
# delta <- seq(from = 40 ,to = 850 ,length.out = 1000 )
# curves.fqcd <- lab.fqcd(TG, argvals = delta,rangeval = c(40,80))
# draw.control = list(col = c("blue","grey"), 
#                    lty = c(1, 1), lwd = c(2, 1))
# #by Walter method
# windows(20,10)
# par(mfrow=c(1,2))
# quantile95.w <- bootstrap.quantile(curves.fqcd, statistic = "h", 
#                                   method = "Walter", smo = 0, 
#                                   nb= 500, alpha = 0.05, quantile = 0.95,draw = TRUE,
#                                   draw.control = draw.control,ylim=c(-3,3),x.co=50,y.co=3,
#                                   main="Statistical h by the method's Walter")
# ## End(Not run)