Assessing the order of dependence for partially exchangeable binary data

Assessing the order of dependence for partially exchangeable binary data

Fernando Quintana and Michael A. Newton .

Technical Report 949, Department of Statistics, University of Wisconsin, Madison.

First issued 1995. Revised September 1996.

Journal of the American Statistical Association , 93, 194--202, 1998.

Abstract:

The problem we consider is how to assess the order of serial dependence within partially exchangeable binary sequences. We obtain exact conditional tests comparing any two orders by finding the conditional distribution of data given certain transition counts. These tests are facilitated with a new Monte Carlo scheme. Asymptotic tests are also discussed. In particular, we show that the likelihood ratio tests have an asymptotic chi-square distribution, thus generalizing the results of Billingsley (1961) for the particular case of Markov chains. We apply these methods to several data sets, and perform a simulation to study their properties.


Key words: conditional simulation, Markov chains, model selection, nonparametric mixtures, multiple binary sequences.
Contact for reprints.