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Bidimensional Random Effect Estimation in Mixed Stochastic Differential Model

Abstract : In this work, a mixed stochastic differential model is studied with two random effects in the drift. We assume that N trajectories are continuously observed throughout a time interval [0, T]. Two directions are investigated. First we estimate the random effects from one trajectory and give a bound of the $L^2$-risk of the estimators. Secondly, we build a nonparametric estimator of the common bivariate density of the random effects. The mean integrated squared error is studied. The performances of the density estimator are illustrated on simulations.
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Charlotte Dion, Valentine Genon-Catalot. Bidimensional Random Effect Estimation in Mixed Stochastic Differential Model. Statistical Inference for Stochastic Processes, Springer Verlag, 2016, 19 (2), pp.131-158. ⟨10.1007/s11203-015-9122-0⟩. ⟨hal-01103303v2⟩

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