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Sur le processus de vraisemblance partielle. (On the partial likelihood process). (French) Zbl 0727.60037
Summary: We propose a definition of partial likelihood processes for general semimartingales, which extends the definition given by the author [Stochastic Processes Appl. 26, 47-71 (1987; Zbl 0632.62088)] and is better fit for statistical problems: we illustrate this statement with some statistical applications. We also prove that partial likelihoods enjoy nice invariance properties: for example they do not change if we replace the basic semimartingale X by $$Y=f(X)$$ with an invertible $$C^ 2$$ function f. Finally, we observe that the asymptotic normality result of the paper cited above remains true in the present setting.

##### MSC:
 60G05 Foundations of stochastic processes 62M99 Inference from stochastic processes 60G48 Generalizations of martingales
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