Maximal Invariants For Lorentz Wishart Models

TL;DR

This paper develops maximal invariant statistics for Lorentz Wishart models to test hypotheses about parameters within Lorentz cones and equality of observations, advancing statistical inference in this geometric setting.

Contribution

It explicitly derives maximal invariants for Lorentz Wishart distributions, enabling hypothesis testing in this specialized geometric context.

Findings

Derived explicit maximal invariant statistics for Lorentz Wishart models

Established testing procedures for sub-Lorentz-cone parameters

Provided methods to test equality of two observations' parameters

Abstract

In this paper we consider two statistical hypotheses for the families of Wishart type distributions. These distributions are analogs of the Wishart distributions defined and parametrized over a Lorentz cone. We test these hypotheses by means of maximal invariant statistics which are explicitly derived in the paper. The testing problems, respectively, concern the hypothesis that parameters are in a sub-Lorentz-cone, and the the hypothesis that two observations have the same parameter.