st.utestR: Test of Uniformity via Rayleigh Statistic on Stiefel Manifold

In RiemStiefel: Inference, Learning, and Optimization on Stiefel Manifold

Description

This function is for hypothesis testing on Stiefel manifold St(p,r) whether the given data is uniformly distributed or not. We provide two options (original and modified) for Rayleigh-type statistics, which both follow Chi-squared distribution of degrees of freedom pr.

Usage

st.utestR(x, method = c("Original", "Modified"))

Arguments

x	either an array of size (p\times r\times n) or a list of length n whose elements are (p\times r) matrix on Stiefel manifold.
method	"original" for conventional Rayleigh statistic or "modified" for 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

mardia_directional_1999RiemStiefel

Examples

## Test of Uniformity for 100 samples from St(10,5)
#  Data Generation
mydat = st.runif(n=100, p=10, r=5, rtype='list')

#  Run Tests using two methods
st.utestR(mydat, method='original')
st.utestR(mydat, method='modified')


## empirical Type 1 error using the same setting as above.
niter   = 10000
counter = rep(0,niter)  # record p-values
for (i in 1:niter){
  X = st.runif(n=100, p=10, r=5, rtype='list')
  counter[i] = ifelse(st.utestR(X)$p.value < 0.05, 1, 0)
  print(paste0("iteration ",i,"/10000 complete..."))
}

## print the result
print(paste0("* empirical Type 1 error for 'st.utestR': ",round(sum(counter/niter),5)))

RiemStiefel documentation built on March 26, 2020, 7:48 p.m.