grassmann.utest: Test of Uniformity on Grassmann Manifold

In Riemann: Learning with Data on Riemannian Manifolds

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"))

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.

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.grassmann

Examples

#-------------------------------------------------------------------
#   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 !

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