Open Access
2016 Palindromic Bernoulli distributions
Giovanni M. Marchetti, Nanny Wermuth
Electron. J. Statist. 10(2): 2435-2460 (2016). DOI: 10.1214/16-EJS1175

Abstract

We introduce and study a subclass of joint Bernoulli distributions which has the palindromic property. For such distributions the vector of joint probabilities is unchanged when the order of the elements is reversed. We prove for binary variables that the palindromic property is equivalent to zero constraints on all odd-order interaction parameters, be it in parameterizations which are log-linear, linear or multivariate logistic. In particular, we derive the one-to-one parametric transformations for these three types of model specifications and give simple closed forms of maximum likelihood estimates. Several special cases are discussed and a case study is described.

Citation

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Giovanni M. Marchetti. Nanny Wermuth. "Palindromic Bernoulli distributions." Electron. J. Statist. 10 (2) 2435 - 2460, 2016. https://doi.org/10.1214/16-EJS1175

Information

Received: 1 November 2015; Published: 2016
First available in Project Euclid: 7 September 2016

zbMATH: 1351.62046
MathSciNet: MR3545465
Digital Object Identifier: 10.1214/16-EJS1175

Subjects:
Primary: 62E10
Secondary: 62H17 , 62H20

Keywords: Central symmetry , linear in probability models , log-linear models , median-dichotomization , multivariate logistic models , odd-order interactions , orthant probabilities

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.10 • No. 2 • 2016
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