fChange (version 0.2.1)

change_fPCA: Change Point Analysis Of Functional Data Via Dimension Reduction

Description

This function tests whether there is a significant change in the mean function of functional data, and it gives an estimate of the location of the change. The procedure will reduce the dimension of the functional data using functional principal component analysis and will use d leading principal curves to carry out the change point analysis. The projection dimension d can be chosen via total variation explained (TVE) using the function pick_dim.

Usage

change_fPCA(fdobj, d, M = 1000, h = 0, plot = FALSE, ...)

Arguments

fdobj

A functional data object of class 'fd'

d

Number of principal components

M

Number of monte carlo simulations to get the critical values. The default value is M=1000

h

The window parameter for the estimation of the long run covariance kernel. The default value is h=0, i.e., it assumes iid data

plot

If TRUE plot of the functional data before and after the estimated change and plot of the estimated change function is given

...

Further arguments to pass

Value

pvalue

An approximate p value for testing whether there is a significant change in the mean function

change

Estimated change location

DataBefore

Data before the estimated change

DataAfter

Data after the estimated change

MeanBefore

Mean function before the estimated change

MeanAfter

Mean function after the estimated change

change_fun

Estimated change function

Details

This functions performs structural break analysis for the functional data using an fPCA based initial dimension reduction. It is recommended that the dimension of the subspace, d, that the functional observations are projected onto should be selected based on TVE using pick_dim.

References

Berkes, I., Gabrys, R.,Hovarth, L. & P. Kokoszka (2009)., Detecting changes in the mean of functional observations Journal of the Royal Statistical Society, Series B 71, 927<U+2013>946

Aue, A., Gabrys, R.,Hovarth, L. & P. Kokoszka (2009)., Estimation of a change-point in the mean function of functional dataJournal of Multivariate Analysis 100, 2254<U+2013>2269.

See Also

change_FF

Examples

# NOT RUN {
# generate functional data
fdata = fun_IID(n=100, nbasis=21)
# insert an artifiical change
data_c = insert_change(fdata, k=21, change_location = 0.5, SNR=1)$fundata
d.hat = pick_dim(data_c, 0.9)$d
change_fPCA(data_c, d=d.hat)$change
# }