Regularity, partial regularity, partial information process, for a filtered statistical model
type: Item
instance of: scholarly article
title: Regularity, partial regularity, partial information process, for a filtered statistical model
zbMATH Open document ID: 0677.62001
DOI: 10.1007/BF01208255
author: Jean Jacod
publication date: 1990-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62A01
Mathematics Subject Classification ID: 62B99
Mathematics Subject Classification ID: 62F99
zbMATH DE Number: 4109818
zbMATH Keywords: regular model
zbMATH Keywords: differentiability of characteristics
zbMATH Keywords: Fisher information process
zbMATH Keywords: semi-parametric models
zbMATH Keywords: partial regularity
zbMATH Keywords: partial likelihoods
zbMATH Keywords: partial information process
zbMATH Keywords: complete information process
zbMATH Keywords: generalization of Cramér-Rao inequality
zbMATH Keywords: partial likelihood processes
zbMATH Keywords: quasi- likelihood processes
zbMATH Keywords: stochastic integrals
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 4109818