change_fPCA: Change Point Analysis Of Functional Data Via Dimension...

In fChange: Change Point Analysis in Functional Data

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

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.

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

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, 927–946

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, 2254–2269.

See Also

change_FF

Examples

# 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

fChange documentation built on May 2, 2019, 6:43 a.m.