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Regularity, partial regularity, partial information process, for a filtered statistical model. (English) Zbl 0677.62001
We define “partial regularity” for a filtered statistical (semi- parametric) model indexed by $$\theta \in {\mathbb{R}}^ d$$, as differentiability in a suitable sense of the partial likelihoods associated with a basic process X. Partial regularity turns out to be equivalent to some sort of differentiability in $$\theta$$ of the characteristics of X. We also prove that regularity of the model implies partial regularity, and we define a “partial information process”, which is smaller than the “complete information process”.
We apply these results to obtain a generalization of Cramér-Rao inequality, and to prove that partial likelihood processes are optimal among all quasi-likelihood processes which are stochastic integrals with respect to the basic process X.
Reviewer: J.Jacod

##### MSC:
 62A01 Foundations and philosophical topics in statistics 62B99 Sufficiency and information 62F99 Parametric inference
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##### References:
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