grassmann.utest: Test of Uniformity on Grassmann Manifold

Description

Given the data on Grassmann manifold \(Gr(k,p)\), it tests whether the data is distributed uniformly.

Usage

grassmann.utest(grobj, method = c("Bing", "BingM"))

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.

Arguments

grobj

a S3 "riemdata" class of Grassmann-valued data.

method

(case-insensitive) name of the test method containing

"Bing": Bingham statistic.

"BingM"

modified Bingham statistic with better order of error.

References

chikuse_statistics_2003Riemann

mardia_directional_1999Riemann

Examples

Run this code

#-------------------------------------------------------------------
#   Compare Bingham's original and modified versions of the test
# 
# Test 1. sample uniformly from Gr(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 = grassmann.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.grassmann(irdat)

## Test 1 : uniform data
grassmann.utest(myobj1, method="Bing")
grassmann.utest(myobj1, method="BingM")

## Tests : iris data
grassmann.utest(myobj2, method="bINg")   # method names are 
grassmann.utest(myobj2, method="BiNgM")  # CASE - INSENSITIVE !