Statistical tests based on Rényi entropy estimation

06/01/2021
by   Mehmet Siddik Cadirci, et al.
1

Entropy and its various generalizations are important in many fields, including mathematical statistics, communication theory, physics and computer science, for characterizing the amount of information associated with a probability distribution. In this paper we propose goodness-of-fit statistics for the multivariate Student and multivariate Pearson type II distributions, based on the maximum entropy principle and a class of estimators for Rényi entropy based on nearest neighbour distances. We prove the L^2-consistency of these statistics using results on the subadditivity of Euclidean functionals on nearest neighbour graphs, and investigate their rate of convergence and asymptotic distribution using Monte Carlo methods. In addition we present a novel iterative method for estimating the shape parameter of the multivariate Student and multivariate Pearson type II distributions.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/21/2020

The entropy based goodness of fit tests for generalized von Mises-Fisher distributions and beyond

We introduce some new classes of unimodal rotational invariant direction...
research
10/13/2020

Entropy-based test for generalized Gaussian distributions

In this paper, we provide the proof of L^2 consistency for the kth neare...
research
06/18/2022

A general Monte Carlo method for multivariate goodness-of-fit testing applied to elliptical families

A general and relatively simple method for construction of multivariate ...
research
04/18/2019

Asymptotic normality of generalized maximum spacing estimators for multivariate observations

In this paper, the maximum spacing method is considered for multivariate...
research
01/13/2021

Multivariate phase-type theory for the site frequency spectrum

Linear functions of the site frequency spectrum (SFS) play a major role ...
research
03/02/2022

A Unifying Framework for Some Directed Distances in Statistics

Density-based directed distances – particularly known as divergences – b...
research
11/08/2019

Estimating Normalizing Constants for Log-Concave Distributions: Algorithms and Lower Bounds

Estimating the normalizing constant of an unnormalized probability distr...

Please sign up or login with your details

Forgot password? Click here to reset