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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.

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