STRONGLY CONSISTENT CODE-BASED IDENTIFICATION AND ORDER ESTIMATION FOR CONSTRAINED FINITE-STATE MODEL CLASSES

Observations are made of data generated by a stationary ergodic finite -alphabet information source according to an unknown statistical model . Two modeling problems, the identification problem and the order esti mation problem, are considered. In the identification problem, one wis hes to decide from the observed data whether the source model belongs to a given model class. In the order estimation problem, one wishes to decide from the observed data to which of infinitely many given model classes the source model belongs. It is required that the given model class in the identification problem and that each given model class i n the order estimation problem be a constrained finite-state model cla ss, which is a type of model class that includes many model classes of information-theoretic interest. Strongly consistent decision rules ar e exhibited in both the identification problem and the order estimatio n problem. The decision rules are code-based in that a model class is chosen based upon how well a certain code for that class encodes the o bserved data. The code used for a model class is based upon the maximu m likelihood code for that class, and asymptotic code performance is g auged by means of a key property of divergence-rate distance.