riem.fanova {Riemann}

Fréchet Analysis of Variance

Description

Given sets of manifold-valued data X^{(1)}_{1:{n_1}}, X^{(2)}_{1:{n_2}}, \ldots, 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

Dubey P, Müller H (2019). “Fréchet analysis of variance for random objects.” Biometrika, 106(4), 803–821. ISSN 0006-3444, 1464-3510.

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)