README.md

Overview

This is an accompanying collection of script files in R and Mathematica, which were used to obtain the numerical results appearing in the paper "A general maximal projection approach to uniformity testing on the hypersphere" (Borodavka, J. and Ebner, B.). The main Mathematica file computes orthonormal bases of spherical harmonics with the help of the Mathematica package HFT.m. The R script files can be used to compute critical values, powers and local Bahadur ARE of the newly proposed test statistic from the aforementioned paper and other competing test statistics under the null hypothesis and for different alternative distributions on the hypersphere. Additionally, there is a script which defines a new alternative distribution on the hypersphere. Each file is complemented with introductory comments, but many more details on implementation are given in the paper.

Usage

You may clone the repository to your local machine via your command-line interface

git clone https://gitlab.kit.edu/jaroslav.borodavka/maximal-projection-gof.git

and then use the scripts in Mathematica or R. Let us give a very simple example on how to used the main R function that was defined in script under the name T_stat_value and corresponds to the newly proposed test statistic T_{n \beta} from the paper. We can first generate a 3-dimensional random sample of a von Mises-Fisher distribution on the sphere with the help of the R package Directional

> data = rvmf(n=100, mu=c(1,0,0), k=0.5)
> head(data)
            [,1]       [,2]       [,3]
[1,]  0.08000159 -0.7790440  0.6218442
[2,] -0.02382322  0.6844500  0.7286705
[3,] -0.01181251  0.5975516 -0.8017434
[4,] -0.37249581 -0.9211856  0.1125339
[5,]  0.04115439  0.6159393 -0.7867179
[6,]  0.39358746 -0.1732262 -0.9028187

and then use the function T_stat_value after specifying the hyperparameter beta obtain the realization of T_{n \beta}

> T_stat_value(data, beta=3)
[1] 2.330788

Authors