fdcov (version 1.1.0)

ksample.gauss: k-sample test for equality of covariance operators

Description

ksample.gauss performs a k-sample test for equality of covariance operators under the assumption that the data arises from a Gaussian process.

Usage

ksample.gauss(dat1, dat2, K = 5)

Arguments

dat1

the first set of data with one entry per row

dat2

the second set of data with one entry per row

K

the number of basis vectors to use, Default is 5.

Value

p-value testing whether or not the two samples have differing covariance operators.

Details

ksample.vstab applies a similar method that has been modified to stabilize the variance. See the reference paper for more details on the mathematics of these methods.

These two methods use the Karhunen-Loeve expansion (eigen expansion for functional data) to represent the data in terms of K eigen-functions. Then a test statistic with asymptotic chi-squared distribution is computed in order to test for the equality of the covariance operators based on the two samples. If K is set to be 0, then the methods determine the number of eigen-functions to retain.

References

Panaretos, Victor M., David Kraus, and John H. Maddocks. "Second-order comparison of Gaussian random functions and the geometry of DNA minicircles." Journal of the American Statistical Association 105.490 (2010): 670-682.

Examples

# NOT RUN {
# Load in phoneme data
library(fds)
# Set up test data
dat1 = t(aa$y)[1:20,];
dat2 = t(sh$y)[1:20,];
dat3 = t(aa$y)[21:40,];
# Compare two disimilar phonemes
# Resulting in a small p-value
ksample.gauss(dat1,dat2,K=5);
ksample.vstab(dat1,dat2,K=5);
# Compare two sets of the same phonemes
# Resulting in a large p-value
ksample.gauss(dat1,dat3,K=5);
ksample.vstab(dat1,dat3,K=5);
# }