Assessing the order of dependence for partially exchangeable binary data

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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.

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