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2018 On penalized estimation for dynamical systems with small noise
Alessandro De Gregorio, Stefano Maria Iacus
Electron. J. Statist. 12(1): 1614-1630 (2018). DOI: 10.1214/18-EJS1436


We consider a dynamical system with small noise for which the drift is parametrized by a finite dimensional parameter. For this model, we consider minimum distance estimation from continuous time observations under $l^{p}$-penalty imposed on the parameters in the spirit of the Lasso approach, with the aim of simultaneous estimation and model selection. We study the consistency and the asymptotic distribution of these Lasso-type estimators for different values of $p$. For $p=1,$ we also consider the adaptive version of the Lasso estimator and establish its oracle properties.


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Alessandro De Gregorio. Stefano Maria Iacus. "On penalized estimation for dynamical systems with small noise." Electron. J. Statist. 12 (1) 1614 - 1630, 2018.


Received: 1 February 2018; Published: 2018
First available in Project Euclid: 26 May 2018

zbMATH: 06875410
MathSciNet: MR3806434
Digital Object Identifier: 10.1214/18-EJS1436

Primary: 62J07 , 62M05
Secondary: 62F12

Keywords: diffusion-type processes , dynamical systems , Inference for stochastic processes , lasso estimation , Model selection , oracle properties


Vol.12 • No. 1 • 2018
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