Palindromic bernoulli distributions
Journal article, 2016

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.

Linear in probability models

Central symmetry

Orthant probabilities

Median-dichotomization

Odd-order interactions

Multivariate logistic models

Log-linear models

Author

Giovanni M. Marchetti

Dipartimento di Statistica

Nanny Wermuth

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Electronic Journal of Statistics

1935-7524 (ISSN)

Vol. 10 2 2435-2460

Subject Categories

Mathematics

DOI

10.1214/16-EJS1175

More information

Created

10/7/2017