Electronic Journal of Statistics

On penalized estimation for dynamical systems with small noise

Alessandro De Gregorio and Stefano Maria Iacus

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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.

Article information

Electron. J. Statist., Volume 12, Number 1 (2018), 1614-1630.

Received: February 2018
First available in Project Euclid: 26 May 2018

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Zentralblatt MATH identifier

Primary: 62M05: Markov processes: estimation 62J07: Ridge regression; shrinkage estimators
Secondary: 62F12: Asymptotic properties of estimators

Dynamical systems lasso estimation model selection inference for stochastic processes diffusion-type processes oracle properties

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De Gregorio, Alessandro; Iacus, Stefano Maria. On penalized estimation for dynamical systems with small noise. Electron. J. Statist. 12 (2018), no. 1, 1614--1630. doi:10.1214/18-EJS1436. https://projecteuclid.org/euclid.ejs/1527300142

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