Nonparametric estimation in a mixed-effect Ornstein–Uhlenbeck model

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• 作者：Charlotte Dion
• 关键词：Stochastic differential equations ; Ornstein–Uhlenbeck process ; Mixed ; effect model ; Nonparametric estimation ; Deconvolution method ; Kernel estimator ; Neuronal data
• 刊名：Metrika
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：79
• 期：8
• 页码：919-951
• 全文大小：1,091 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Probability Theory and Stochastic Processes
  Economic Theory
  
• 出版者：Physica Verlag, An Imprint of Springer-Verlag GmbH
• ISSN：1435-926X
• 卷排序：79

文摘

Two adaptive nonparametric procedures are proposed to estimate the density of the random effects in a mixed-effect Ornstein–Uhlenbeck model. First a kernel estimator is introduced with a new bandwidth selection method developed recently by Goldenshluger and Lepski (Ann Stat 39:1608–1632, 2011). Then, we adapt an estimator from Comte et al. (Stoch Process Appl 7:2522–2551, 2013) in the framework of small time interval of observation. More precisely, we propose an estimator that uses deconvolution tools and depends on two tuning parameters to be chosen in a data-driven way. The selection of these two parameters is achieved through a two-dimensional penalized criterion. For both adaptive estimators, risk bounds are provided in terms of integrated \(\mathbb {L}^2\)-error. The estimators are evaluated on simulations and show good results. Finally, these nonparametric estimators are applied to neuronal data and are compared with previous parametric estimations.