Nonparametric estimation for stochastic differential equations with random effects

F. Comte, V. Genon-Catalot and A. Samson

Stochastic Processes and their Applications, 2013, vol. 123, issue 7, 2522-2551

Abstract: We consider N independent stochastic processes (Xj(t),t∈[0,T]), j=1,…,N, defined by a one-dimensional stochastic differential equation with coefficients depending on a random variable ϕj and study the nonparametric estimation of the density of the random effect ϕj in two kinds of mixed models. A multiplicative random effect and an additive random effect are successively considered. In each case, we build kernel and deconvolution estimators and study their L2-risk. Asymptotic properties are evaluated as N tends to infinity for fixed T or for T=T(N) tending to infinity with N. For T(N)=N2, adaptive estimators are built. Estimators are implemented on simulated data for several examples.

Keywords: Diffusion process; Mixed models; Nonparametric estimation; Random effects (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2013.04.009

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