Parametric Partially Exchangeable Models forMultiple Binary

In this paper we discuss models for multiple binary sequences using de Finetti's notions of exchangeability and partial exchangeability as a cornerstone for model building. Thus, we assume each sequence to be a Markov chain conditional on some random transition matrix. This construction is seen as an extension of models based on Polya urns. We consider two particular problems in which the distribution of random eeects is indexed by a parameter. We rst show that the likelihood hypoconverges to an \ideal" but unobserved likelihood of transition matrices, when sequence lengths go to 1 for a xed number of experimental units. This permits us to study consistency of the likelihood maximizer to the ideal maximum likelihood estimator. Secondly, we introduce a \naive" estimation approach in which we estimate transition matrices and pretend these are actual draws from the mixing measure. Under smoothness conditions, the approach yields strongly consistent, asymptotically normal and eecient estimates of also shown to hold when both k, the number of sequences and their lengths n k go to 1. Conditions are given so that no growth rates are needed for n k .