fdcov (version 1.1.0)

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

Description

ksample.com performs a k-sample test for equality of covariance operators using concentration inequalities.

Usage

ksample.com(dat, grp, p = 1, alpha = 0.05, scl1 = 1, scl2 = 1)

Arguments

dat

(n X m) data matrix of n samples of m long vectors.

grp

n long vector of group labels.

p

p-Schatten norm in [1,Inf], Default is 1. (see Details)

alpha

the desired size of the test, Default is 0.05.

scl1

scales the deviation part of the concentration inequality. (see Details)

scl2

scales the Rademacher part of the concentration inequality. (see Details)

Value

Boolean value for whether or not the test believes the alternative hypothesis is true. ( i.e. Does there exist at least two categories of the k whose covariance operators are not equal? )

Details

This function tests for the equality of k covariance operators given k sets of functional data. It makes use of Talagrand's concentration inequality in the Banach space setting. The argument p specifies the p-Schatten norm used in the test. As detailed in Kashlak et al (2016), the most power is achieved using the trace class norm (p=1), which is the default value.

This test is inherently conservative as it constructed by concatenating many concentration inequalities together. Consequently, the method may be tuned by adjusting the arguments scl1 and scl2 to achieve the desired empirical size for the users specific data set. Otherwise, it can be used as a quick first pass before a more powerful but more computational test, such as specifically ksample.perm, is run. More information on tuning this method can be found in the reference.

References

Kashlak, Adam B, John AD Aston, and Richard Nickl (2016). "Inference on covariance operators via concentration inequalities: k-sample tests, classification, and clustering via Rademacher complexities", (in review)

Examples

# NOT RUN {
# Load in phoneme data
library(fds)
# Setup data arrays
dat1 = rbind( t(aa$y)[1:20,], t(sh$y)[1:20,] );
dat2 = rbind( t(aa$y)[1:20,], t(ao$y)[1:20,] );
dat3 = rbind( dat1, t(ao$y)[1:20,] );
# Setup group labels
grp1 = gl(2,20);
grp2 = gl(2,20);
grp3 = gl(3,20);
# Compare two disimilar phonemes (should return TRUE)
ksample.com(dat1,grp1);
# Compare two similar phonemes (should return FALSE)
ksample.com(dat2,grp2);
# Compare three phonemes (should return TRUE)
ksample.com(dat3,grp3);
# }