fChange (version 0.2.1)

trace_change: Testing changes in the trace of the covariance operator in functional data

Description

This function tests and detects changes in the trace of the covariance operator.

Usage

trace_change(fdobj, mean_change = FALSE, delta = 0.1, M = 1000)

Arguments

fdobj

A functional data object of class 'fd'

mean_change

If TRUE then the data is centered considering the change in the mean function.

delta

Trimming parameter to estimate the covariance function using partial sum estimates.

M

Number of monte carlo simulations used to get the critical values. The default value is M=1000 value is h=2.

Value

pvalue

Approximate p value for testing whether there is a significant change in the desired eigenvalue of the covariance operator

change

Estimated change location

trace_before

Estimated trace before the change

trace_after

Estimated trace after the change

Details

This function dates and detects changes in trace of the covariance function. This can be interpreted as the changes in the total variation of the the functional data. Trace is defined as the infinite sum of the eigenvalues of the covariance operator and for the sake of implementation purpose, the sum is truncated up to the total number of basis functions that defines the functional data at hand. The critical values are approximated via M Monte Carlo simulations.

Examples

# NOT RUN {
# generate functional data
fdata = fun_IID(n=100, nbasis=21)
trace_change(fdata)
# }