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.

Palindromic bernoulli distributions / Marchetti, Giovanni M.; Wermuth, Nanny. - In: ELECTRONIC JOURNAL OF STATISTICS. - ISSN 1935-7524. - ELETTRONICO. - 10:(2016), pp. 2435-2460. [10.1214/16-EJS1175]

Palindromic bernoulli distributions

MARCHETTI, GIOVANNI MARIA;
2016

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.
2016
10
2435
2460
Marchetti, Giovanni M.; Wermuth, Nanny
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1075470
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