stiefel.utest: Test of Uniformity on Stiefel Manifold

In Riemann: Learning with Data on Riemannian Manifolds

Test of Uniformity on Stiefel Manifold

Description

Given the data on Stiefel manifold St(k,p), it tests whether the data is distributed uniformly.

Usage

stiefel.utest(stobj, method = c("Rayleigh", "RayleighM"))

Arguments

stobj	a S3 "riemdata" class for N Stiefel-valued data.
method	(case-insensitive) name of the test method containing "Rayleigh" original Rayleigh statistic. "RayleighM" modified Rayleigh statistic with better order of error.

Value

a (list) object of S3 class htest containing:

statistic

a test statistic.

p.value

p-value under H_0.

alternative

alternative hypothesis.

method

name of the test.

data.name

name(s) of provided sample data.

References

\insertRef

chikuse_statistics_2003Riemann

\insertRef

mardia_directional_1999Riemann

See Also

wrap.stiefel

Examples

#-------------------------------------------------------------------
#   Compare Rayleigh's original and modified versions of the test
# 
# Test 1. sample uniformly from St(2,4)
# Test 2. use perturbed principal components from 'iris' data in R^4
#         which is concentrated around a point to reject H0.
#-------------------------------------------------------------------
## DATA GENERATION
#  1. uniform data
myobj1 = stiefel.runif(n=100, k=2, p=4)

#  2. perturbed principal components
data(iris)
irdat = list()
for (n in 1:100){
   tmpdata    = iris[1:50,1:4] + matrix(rnorm(50*4,sd=0.5),ncol=4)
   irdat[[n]] = eigen(cov(tmpdata))$vectors[,1:2]
}
myobj2 = wrap.stiefel(irdat)

## TEST
#  1. uniform data
stiefel.utest(myobj1, method="Rayleigh")
stiefel.utest(myobj1, method="RayleighM")

#  2. concentrated data
stiefel.utest(myobj2, method="rayleIgh")   # method names are 
stiefel.utest(myobj2, method="raYleiGhM")  # CASE - INSENSITIVE !

Riemann documentation built on March 18, 2022, 7:55 p.m.