scb.mean {SCBmeanfd}

Build Simultaneous Confidence Bands for Mean Functions

Description

Fit a local linear estimator and build simultaneous confidence bands (SCB) for the mean of functional data.

Usage

scb.mean(x, y, bandwidth, level = .95, degree = 1, 
	scbtype = c("normal","bootstrap","both","no"), gridsize = length(x), 
	keep.y = TRUE, nrep = 2e4, nboot = 5e3, parallel = c("no", "multicore", "snow"), 
	ncpus = getOption("boot.ncpus",1L), cl = NULL)

Arguments

x

a numeric vector of x data. Missing values are not accepted.

y

a matrix or data frame with functional observations (= curves) stored in rows. The number of columns of y must match the length of x. Missing values are not accepted.

bandwidth

the kernel bandwidth smoothing parameter.

level

the level of the simultaneous confidence bands.

degree

the degree of the local polynomial fit.

scbtype

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

gridsize

the size of the grid used to evaluate the mean function estimates and SCB. Defaults to length(x).

keep.y

logical; if TRUE, keep y in the result.

nrep

number of replicates for the Gaussian SCB method (20,000 by default).

nboot

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

parallel

the computation method for the SCB. By default, computations are sequential ("no"). The bootstrap method uses function boot and can be run in parallel using the package parallel. In this case both options "multicore" and "snow" are available.

ncpus

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

cl

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

Details

The local polynomial fitting uses a standard normal kernel and is implemented via the locpoly function. Bootstrap SCB are implemented with the boot function and typically require more computation time than normal SCB.

Value

An object of class "SCBand". To accommodate the different functions creating objects of this class (scb.mean, scb.model, and scb.equal), some components of the object are set to NULL. The component list is:

x

the x data.

y

the y data if keep.y is TRUE, else NULL.

call

the function call.

model

NULL.

par

NULL.

nonpar

a nonparametric estimate.

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 type.

teststat

NULL.

pnorm

NULL.

pboot

NULL.

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 if nonnull, else length(x).

nrep

the argument nrep.

nboot

the argument nboot.

Depending on the value of scbtype, some of the fields qnorm, normscb, nrep, qboot, normboot and nboot may be NULL.

References

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

See Also

scb.equal, scb.model

Examples

## Not run: 
## Plasma citrate data
data(plasma)
time <- 8:21
h <- cv.select(time, plasma, 1, c(.5, 1))
scbplasma <- scb.mean(time, plasma, bandwidth = h, scbtype = "both", gridsize = 100)
scbplasma
plot(scbplasma, cex = .2, legend.cex = .85, xlab = "Time", ylab = "Concentration", 
  main = "Plasma citrate data")

## End(Not run)