Electronic Journal of Statistics

Palindromic Bernoulli distributions

Giovanni M. Marchetti and Nanny Wermuth

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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.

Article information

Electron. J. Statist., Volume 10, Number 2 (2016), 2435-2460.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62E10: Characterization and structure theory
Secondary: 62H17: Contingency tables 62H20: Measures of association (correlation, canonical correlation, etc.)

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


Marchetti, Giovanni M.; Wermuth, Nanny. Palindromic Bernoulli distributions. Electron. J. Statist. 10 (2016), no. 2, 2435--2460. doi:10.1214/16-EJS1175. https://projecteuclid.org/euclid.ejs/1473276076

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