Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 9, Number 1 (2015), 475-491.
Smoothness of marginal log-linear parameterizations
We provide results demonstrating the smoothness of some marginal log-linear parameterizations for distributions on multi-way contingency tables. First we give an analytical relationship between log-linear parameters defined within different margins, and use this to prove that some parameterizations are equivalent to ones already known to be smooth. Second we construct an iterative method for recovering joint probability distributions from marginal log-linear pieces, and prove its correctness in particular cases. Finally we use Markov chain theory to prove that certain cyclic conditional parameterizations are also smooth. These results are applied to show that certain conditional independence models are curved exponential families.
Electron. J. Statist., Volume 9, Number 1 (2015), 475-491.
First available in Project Euclid: 24 March 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62H17: Contingency tables
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.)
Evans, Robin J. Smoothness of marginal log-linear parameterizations. Electron. J. Statist. 9 (2015), no. 1, 475--491. doi:10.1214/15-EJS1009. https://projecteuclid.org/euclid.ejs/1427203126