Statistical Inference for Quadratic Rényi Entropy

Kernelized Rényi distance for subset selection and similarity scoring

Rényi entropy refers to a generalized class of entropies that have been used in several applications. In this work, we derive a non-parametric distance between distributions based on the quadratic Rényi entropy. The distributions are estimated via Parzen density estimates. The quadratic complexity of the distance evaluation is mitigated with GPUbased parallelization. This results in an efficien...

On the Statistical Estimation of Rényi Entropies

Estimating entropies is important in many fields including statistical physics, machine learning and statistics. While the Shannon logarithmic entropy is the most fundamental, other Rényi entropies are also of importance. In this paper, we derive a bias corrected estimator for a subset of Rényi entropies. The advantage of the estimator is demonstrated via theoretical and experimental considerat...

A Note on Maximum Rényi Entropy OWA Problem

Bayesian Statistical Inference on Elliptical Matrix Distributions

In this paper we are concerned with Bayesian statistical inference for a class of elliptical distributions with parameters + and 7. Under a noninformative prior distribution, we obtain the posterior distribution, posterior mean, and generalized maximim likelihood estimators of + and 7. Under the entropy loss and quadratic loss, the best Bayesian estimators of 7 are derived as well. Some applica...

Power law distribution of Rényi entropy for equilibrium systems having nonadditive energy

Using Rényi entropy, an alternative statistics to Tsallis one for nonextensive systems at equilibrium is discussed. We show that it is possible to have the q-exponential distribution function for equilibrium nonextensive systems having nonadditive energy but additive entropy. PACS : 02.50.-r, 05.20.-y, 05.70.-a