On Supra-Bayesian Weighted Combination of Available Data Determined by Kerridge Inaccuracy and Entropy

Abstract

Every process in our environment can be described with a statistical model containing inner properties expressed by parameters. These are usually unknown and the determination of their values is of interest in the statistical branch called parameter estimation. This branch involves many methods solving different estimation cases, e.g. the estimation of location and scale parameters. To obtain the parameter estimate we exploit the data given by data sources. In particular, the estimate is their combination. Improvement of the parameter estimates involve the assignment of the weights to the data sources resulting in a weighted combination of data. Unfortunately this approach brings difficulties regarding the determination of the weights and their subjective affection. In recently introduced Supra-Bayesian approach it is proposed to use the Kerridge inaccuracy and the maximum entropy principle to overcome the problem of subjective influence. In this paper we focus on the derivation of the weights arisen within the Supra-Bayesian approach and on the simulation study of their behaviour and the behaviour of the final estimate.