Nonparametric estimation for stochastic differential equations with random effects

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• 作者：F. Comte ; ^{fabienne.comte@parisdescartes.fr} ; V. Genon-Catalot ^{valentine.genon-catalot@parisdescartes.fr} ; A. Samson ^{adeline.samson@parisdescartes.fr}
• 关键词：62G07 ; 62M05
• 刊名：Stochastic Processes and their Applications
• 出版年：2013
• 出版时间：July, 2013
• 年：2013
• 卷：123
• 期：7
• 页码：2522-2551
• 全文大小：1627 K

文摘

We consider independent stochastic processes , , defined by a one-dimensional stochastic differential equation with coefficients depending on a random variable and study the nonparametric estimation of the density of the random effect 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 -risk. Asymptotic properties are evaluated as tends to infinity for fixed or for tending to infinity with . For , adaptive estimators are built. Estimators are implemented on simulated data for several examples.