Nonparametric estimation for stochastic differential equations with random effects

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Comte, F.¹  Genon-Catalot, V.¹  Samson, A.¹ 

[1] Univ Paris 05, CNRS, UMR 8145, Sorbonne Paris Cite,MAP5, Paris, France

关键词: Diffusion process;    Mixed models;    Nonparametric estimation;    Random effects;   

DOI  :  10.1016/j.spa.2013.04.009

来源: Elsevier

【 摘 要 】

We consider N independent stochastic processes (X (j)(t), t is an element of [0, T]), j = 1, ... , N, defined by a one-dimensional stochastic differential equation with coefficients depending on a random variable phi(j) and study the nonparametric estimation of the density of the random effect phi(j) 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 L-2-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) = N-2, adaptive estimators are built. Estimators are implemented on simulated data for several examples. (c) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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