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Nonparametric estimation in a mixed-effect Ornstein–Uhlenbeck model

Charlotte Dion ()
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Charlotte Dion: Université Grenoble Alpes

Metrika: International Journal for Theoretical and Applied Statistics, 2016, vol. 79, issue 8, 919-951

Abstract: Abstract 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 $$\mathbb {L}^2$$ 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.

Keywords: Stochastic differential equations; Ornstein–Uhlenbeck process; Mixed-effect model; Nonparametric estimation; Deconvolution method; Kernel estimator; Neuronal data; 62G07; 62M05 (search for similar items in EconPapers)
Date: 2016
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