2021/06/01 by Mehmet Sıddık Çadırcı, Mehmet Siddik Cadirci, Dafydd Evans +6 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Bayesian Methods and Mixture Models #Combinatorics #Entropy (arrow of time) #Entropy estimation #Estimator #FOS: Mathematics #Mathematics #Multivariate statistics #Physics #Principle of maximum entropy #Rényi entropy #Statistical Mechanics and Entropy #Statistical Methods and Inference #Statistical physics #Statistics #Statistics Theory (math.ST) #Subadditivity #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.2106.00453
published in arXiv (Cornell University) (Cornell University)
arxiv created 2021/06/01 · openalex publication_date 2021/06/01 · arxiv updated 2021/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 L2-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.