关于马氏序估计的最小罚
On the minimal penalty for Markov order estimation
摘要：
我们发现，大规模的典型性的马尔可夫样本路径意味着似然比统计量满足重对数律一致相同的规模。因此，惩罚似然马尔可夫顺序估计是强一致的处罚增长缓慢的log log n时，施加的上界的顺序，可以快速增长的log n。我们的证明方法，使用技术从经验过程理论，不依赖于显式表达式的最大似然估计在马尔可夫的情况下，因此可以适用于其他设置。
英文摘要：
We show that large-scale typicality of Markov sample paths implies that the likelihood ratio statistic satisfies a law of iterated logarithm uniformly to the same scale. As a consequence, the penalized likelihood Markov order estimator is strongly consistent for penalties growing as slowly as log log n when an upper bound is imposed on the order which may grow as rapidly as log n. Our method of proof, using techniques from empirical process theory, does not rely on the explicit expression for the maximum likelihood estimator in the Markov case and could therefore be applicable in other settings.
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