KSCovL2WS: L2-norm test using W-S approximation for equality of several covariance functions

Description

L2-norm test of equality of several covariance functions, using the naive or bias-reduced method (Welch--Satterthwaite approximation) to approximate the null distribution.

Usage

KSCovL2WS(data, apprflag = 0, method = 1, Nsim = 1000)

Arguments

data

The list variable containing k groups of presmoothed functional observations. Each element of the list is a p (number sampling points) by n (sample size) matrix.

apprflag

Approximation method, 0: naive method, 1: bias-reduced method.

method

placeholder for L2 resampling method, for testing purpose, should not use currently.

Nsim

placeholder for L2 resampling method, for testing purpose, should not use currently.

Value

The p-value of the test.

Details

L2-norm test of equality of several covariance functions. The null distribution will be approximated by a scaled chi-squared random variable. Two approximation methods are implemented: naive method and bias-reduced method, which work for Gaussian data only. The bias-reduced method is more accurate than the naive method for Gaussian data. The input functional data should have been registered and presmoothed. See Ramsay and Silverman (2005) Ch.7 for registration, and Zhang (2013) Ch.3 for presmoothing. Tools for preprocessing raw functional data are available in R package fda, see also Ramsay et al. (2009).

References

ZHANG (2013), GUO et al. (2016), RAMSAY and SILVERMAN (2005), RAMSAY et al. (2009).

Examples

Run this code

fdata<-list();
fdata[[1]]<-matrix(rnorm(200),20,10);
fdata[[1]]<-matrix(rnorm(300),20,15);
KSCovL2WS(fdata, 0)
KSCovL2WS(fdata, 1)

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