scb.equal: Compare Two Mean Functions

Description

This two-sample test builds simultaneous confidence bands (SCB) for the difference between two population mean functions and retains the equality assumption if the null function is contained in the bands. Equivalently, SCB are built around one of the local linear estimates (the one for say, population 1), and the equality hypothesis is accepted if the other estimate (the one for population 2) lies within the bands.

Usage

scb.equal(x, y, bandwidth, level = 0.05, scbtype = c("normal", "bootstrap",  "both", "no"), gridsize, keep.y = TRUE, nrep = NULL, nboot = NULL,  parallel = c("no", "multicore", "snow"), ncpus = getOption( "boot.ncpus", 1L), cl = NULL)

Arguments

a list of length 2 containing numeric vectors of x data; if the two samples are observed on the same grid, x can be specified as a single vector. x must be a uniform grid; missing values are not accepted.

a list of length 2 containing matrices or data frames with functional observations (= curves) stored in rows. The number of columns of each component of y must match the length of the corresponding x. Missing values are not accepted.

bandwidth

the kernel bandwidth smoothing parameters (numeric vector of length 2).

level

the significance level of the test (default = .05).

scbtype

the type of simultaneous confidence bands to build: "normal", "bootstrap", "both", or "no".

gridsize

the size of the grid over which the mean function is to be estimated. Defaults to the length of x.

keep.y

logical; if TRUE, keep y in the result.

nrep

the number of replicates for the normal SCB method (default = 20,000).

nboot

the number of replicates for the bootstrap SCB method (default = 5,000).

parallel

the computation method for the bootstrap SCB. By default, computations are sequential ("no"). The function boot is used and can be run in parallel using the package parallel. Both options "multicore" and "snow" are available for parallel computing.

ncpus

the number of cores to use for parallel computing if parallel = "multicore".

the name of the cluster to use for parallel computing if parallel = "snow".

Value

x: the argument x.
y: if keep.y is TRUE, the argument y, else NULL.
call: the function call.
model: NULL.
par: NULL.
nonpar: a list of two local linear estimates, one for each population.
bandwidth: the argument bandwidth.
degree: the degree of local polynomial used. Currently, only local linear estimation is supported.
level: the argument level.
scbtype: the argument scbtype.
teststat: the test statistic.
pnorm: the p value for the normal-based statistical test.
pboot: the p value for the boostrap-based statistical test.
qnorm: the quantile used to build the normal SCB.
qboot: the quantile used to build the bootstrap SCB.
normscb: a matrix containing the normal SCB stored in columns.
bootscb: a matrix containing the bootstrap SCB stored in columns.
gridsize: the argument gridsize, or length(x) if no argument was specified.
nrep: the argument nrep.
nboot: the argument nboot.

References

Degras, D. (2011). Simultaneous confidence bands for nonparametric regression with functional data. Statistica Sinica, 21, 1735--1765.

Examples

Run this code

## Not run: 
# # Phoneme data: compare the mean log-periodograms 
# # for phonemes "aa" as the vowel in "dark" and "ao" 
# # as the first vowel in "water"
# data(phoneme)
# n <- nrow(phoneme)
# N <- ncol(phoneme) 
# classes <- split(1:n,phoneme[,N])
# names(classes) <- c("sh", "iy", "dcl", "aa", "ao")
# freq    <- 1:150
# compare.aa.ao <- scb.equal(freq, list(phoneme[classes$aa,-N], 
#   phoneme[classes$ao,-N]), bandwidth = c(.75, .75), scbtype = "both", nboot = 2e3)
# summary(compare.aa.ao)
# ## End(Not run)