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Pré-Publication, Document De Travail Année : 2015

Nonparametric estimation in a mixed-effect Ornstein-Uhlenbeck model

Charlotte Dion
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Résumé

Two adaptive nonparametric procedures are proposed to estimate the density of the random effects in a mixed-effect Ornstein-Uhlenbeck model. First an estimator using deconvolution tools is introduced, which depends on two tuning parameters to be chosen in a data-driven way. The selection of these two parameters is achieved with a Goldenshluger and Lepski's method, extended to this particular case with a new two-dimensional penalized criterion. Then, we propose a kernel estimator of the density of the random effect, with a new bandwidth selection method. For both data driven estimators, risk bounds are provided in term of integrated $\mathbb{L}^2$-error. The estimators are evaluated on simulations and show good results. Finally, these nonparametric estimators are applied to a neuronal database of interspike intervals, and are compared with a previous parametric estimation.
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Dates et versions

hal-01023300 , version 1 (11-07-2014)
hal-01023300 , version 2 (21-11-2014)
hal-01023300 , version 3 (05-12-2014)
hal-01023300 , version 4 (22-05-2015)
hal-01023300 , version 5 (07-02-2016)

Identifiants

  • HAL Id : hal-01023300 , version 4

Citer

Charlotte Dion. Nonparametric estimation in a mixed-effect Ornstein-Uhlenbeck model. 2015. ⟨hal-01023300v4⟩

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