stiefel.utest: 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

chikuse_statistics_2003Riemann

mardia_directional_1999Riemann

Examples

Run this code

# NOT RUN {
#-------------------------------------------------------------------
#   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 !

# }