Electronic Journal of Statistics

On penalized estimation for dynamical systems with small noise

Alessandro De Gregorio and Stefano Maria Iacus

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1527300142

Digital Object Identifier
doi:10.1214/18-EJS1436

Mathematical Reviews number (MathSciNet)
MR3806434

Zentralblatt MATH identifier
06875410

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

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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