Bidimensional Random Effect Estimation in Mixed Stochastic Differential Model

Charlotte Dion (1, 2) , Valentine Genon-Catalot (2)

1 SAM - Statistique Apprentissage Machine
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

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.

Keywords: mixed-effects models; stochastic differential equations; kernel estimator; mean integrated squared error; density estimation; Adaptive bandwidth

Domains: Statistics [math.ST]

Charlotte Dion, Valentine Genon-Catalot. Bidimensional Random Effect Estimation in Mixed Stochastic Differential Model. 2015. ⟨hal-01103303v1⟩