Statistical Topics and Stochastic Models for Dependent Data with Applications

10Inferential Statistics Based on Measures of Information and Divergence

In this chapter, we attempt an overview of measures of information and divergence. Many of the most known measures and some of their most important properties are briefly presented. We discuss the use of measures of divergence in model selection criteria and in goodness-of-fit tests for multinomial distributions. Emphasis is given to the newly proposed double index (Φ, α) test of fit, which through the two indices involved provides greater flexibility to the researcher for inferential purposes and combines under a single umbrella most of the well-known test statistics previously investigated.

10.1. Introduction

Divergence measures have numerous applications in statistical inference and can be applied in various fields such as signal processing and pattern recognition (Bekara et al. 2006), speech recognition (Qiao and Minematsu 2010), clustering (Fischer 2010), finance and economics (Toma and Leoni-Aubin 2014), analysis of contingency tables (Alin and Kurt 2008; Kateri 2018), model selection (Akaike 1973; Cavanaugh 2004; Shang and Cavanaugh 2008; Mattheou et al. 2009; Mantalos et al. 2010; Toma 2014), parameter estimation (Neath et al. 2015; Jiménez-Gamero and Batsidis 2017), goodness-of-fit tests (Toma and Leoni-Aubin 2010; Stehlík et al. 2014, 2018), etc.

Although, in special cases, physical data generating mechanisms suggest a good probability model, in general, we do not have sufficient knowledge of ...