Pathwise Fluctuations of Likelihood Ratios and Consistent Order Estimation by Elisabeth Gassiat
نویسنده
چکیده
Consider an i.i.d. sequence of random variables whose distribution f lies in one of a nested family of models Mq , q ≥ 1. We obtain a sharp characterization of the pathwise fluctuations of the generalized likelihood ratio statistic under entropy assumptions on the model classes Mq. Moreover, we develop a technique to obtain local entropy bounds from global entropy computations, so that these results can be applied in models with non-regular geometric structure. Finally, the results are applied to prove strong consistency and to identify minimal penalties for penalized likelihood order estimators in the absence of prior upper bounds on the model order and the underlying parameter set. Location mixture models, which possess a notoriously complicated geometric structure, are used as a case study throughout the paper, and the requisite geometric analysis is of independent interest.
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