# riem.fanova: Fréchet Analysis of Variance In Riemann: Learning with Data on Riemannian Manifolds

 riem.fanova R Documentation

## Fréchet Analysis of Variance

### Description

Given sets of manifold-valued data X^{(1)}_{1:{n_1}}, X^{(2)}_{1:{n_2}}, …, X^{(m)}_{1:{n_m}}, performs analysis of variance to test equality of distributions. This means, small p-value implies that at least one of the equalities does not hold.

### Usage

```riem.fanova(..., maxiter = 50, eps = 1e-05)

riem.fanovaP(..., maxiter = 50, eps = 1e-05, nperm = 99)
```

### Arguments

 `...` S3 objects of `riemdata` class for manifold-valued data. `maxiter` maximum number of iterations to be run. `eps` tolerance level for stopping criterion. `nperm` the number of permutations for resampling-based test.

### 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

dubey_frechet_2019Riemann

### Examples

```#-------------------------------------------------------------------
#            Example on Sphere : Uniform Samples
#
#  Each of 4 classes consists of 20 uniform samples from uniform
#  density on 2-dimensional sphere S^2 in R^3.
#-------------------------------------------------------------------
## PREPARE DATA OF 4 CLASSES
ndata  = 200
class1 = list()
class2 = list()
class3 = list()
class4 = list()
for (i in 1:ndata){
tmpxy = matrix(rnorm(4*2, sd=0.1), ncol=2)
tmpz  = rep(1,4)
tmp3d = cbind(tmpxy, tmpz)
tmp  = tmp3d/sqrt(rowSums(tmp3d^2))

class1[[i]] = tmp[1,]
class2[[i]] = tmp[2,]
class3[[i]] = tmp[3,]
class4[[i]] = tmp[4,]
}
obj1 = wrap.sphere(class1)
obj2 = wrap.sphere(class2)
obj3 = wrap.sphere(class3)
obj4 = wrap.sphere(class4)

## RUN THE ASYMPTOTIC TEST
riem.fanova(obj1, obj2, obj3, obj4)

## RUN THE PERMUTATION TEST WITH MANY PERMUTATIONS
riem.fanovaP(obj1, obj2, obj3, obj4, nperm=999)

```

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