Riemann (version 0.1.4)

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"))

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

chikuse_statistics_2003Riemann

mardia_directional_1999Riemann

See Also

wrap.grassmann

Examples

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

# }