Summary
We define “partial regularity” for a filtered statistical (semi-parametric) model indexed by θ∈ℝd, as differentiability in a suitable sense of the partial likelihoods associated with a basic processX. Partial regularity turns out to be equivalent to some sort of differentiability in θ of the characteristics ofX. 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 Cramer-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 processX.
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Jacod, J. Regularity, partial regularity, partial information process, for a filtered statistical model. Probab. Th. Rel. Fields 86, 305–335 (1990). https://doi.org/10.1007/BF01208255
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DOI: https://doi.org/10.1007/BF01208255
Keywords
- Statistical Model
- Information Process
- Stochastic Process
- Probability Theory
- Mathematical Biology