Bidimensional random effect estimation in mixed stochastic differential model

Article

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 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.

Keywords

Adaptive bandwidth Density estimation Kernel estimator  Mean integrated squared error Mixed-effects models  Stochastic differential equations 

AMS Subject Classification

62M05 62G07 60J60 

Supplementary material

11203_2015_9122_MOESM1_ESM.pdf (57 kb)
Supplementary material 1 (pdf 57 KB)

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.LJK, UMR CNRS 5224Université Joseph FourierGrenobleFrance
  2. 2.MAP5, UMR CNRS 8145Université Paris Descartes, Sorbonne Paris CitéParisFrance

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