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 large 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.
Adaptive bandwidth Density estimation Kernel estimator Mean integrated squared error Mixed-effects models Stochastic differential equations
AMS Subject Classification
62M05 62G07 60J60
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