# stiefel.utest: Test of Uniformity on Stiefel Manifold In Riemann: Learning with Data on Riemannian Manifolds

 stiefel.utest R Documentation

## 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

\insertRef

chikuse_statistics_2003Riemann

\insertRef

mardia_directional_1999Riemann

`wrap.stiefel`

### Examples

```#-------------------------------------------------------------------
#   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 !

```

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