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Last data update: 2014.03.03

R: Compute functional (FDA) Mandel's h and k statistics

bootstrap.quantile

R Documentation

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, ...)

## Default S3 method:
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, ...)

## S3 method for class 'lab.fqcd'
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, ...)

## S3 method for class 'bootstrap.quantile'
print(x, ...)

## S3 method for class 'bootstrap.quantile'
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