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Foundations of Info-MetricsModeling, Inference, and Imperfect Information$
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Amos Golan

Print publication date: 2017

Print ISBN-13: 9780199349524

Published to Oxford Scholarship Online: November 2017

DOI: 10.1093/oso/9780199349524.001.0001

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Info-Metrics and Statistical Inference

Info-Metrics and Statistical Inference

Discrete Problems

Chapter:
(p.334) 12 Info-Metrics and Statistical Inference
Source:
Foundations of Info-Metrics
Author(s):

Amos Golan

Publisher:
Oxford University Press
DOI:10.1093/oso/9780199349524.003.0012

This chapter is the first of a two-chapter sequence looking into the relationship between info-metrics and the more familiar statistical methods of inference, with an emphasis on information-theoretic methods. In this chapter I concentrate on discrete models. The relationship between info-metrics and information-theoretic statistical methods is established via duality theory, which provides a way for specifying all inferential methods as constrained optimization models. Since the objective here is to compare different approaches and philosophies, the analysis and examples are kept simple. A main result is that, for discrete problems, the maximum-likelihood approach is a special case of the info-metrics framework. To show this, I reconstruct the likelihood model as a constrained optimization problem. The relevant diagnostics and statistics are developed and discussed. I conclude the chapter with a detailed summary of the benefits of info-metrics for inference of discrete problems. Two detailed case studies are provided.

Keywords:   concentrated model, constrained optimization, discrete choice problems, generalized likelihood, info-metrics applications, logit, marginal effects, maximum likelihood

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