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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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