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Adaptive Lasso-Type Estimation For Multivariate Diffusion Processes

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  • De Gregorio, Alessandro
  • Iacus, Stefano M.

Abstract

The least absolute shrinkage and selection operator (LASSO) is a widely used statistical methodology for simultaneous estimation and variable selection. It is a shrinkage estimation method that allows one to select parsimonious models. In other words, this method estimates the redundant parameters as zero in the large samples and reduces variance of estimates. In recent years, many authors analyzed this technique from a theoretical and applied point of view. We introduce and study the adaptive LASSO problem for discretely observed multivariate diffusion processes. We prove oracle properties and also derive the asymptotic distribution of the LASSO estimator. This is a nontrivial extension of previous results by Wang and Leng (2007, Journal of the American Statistical Association , 102(479), 1039–1048) on LASSO estimation because of different rates of convergence of the estimators in the drift and diffusion coefficients. We perform simulations and real data analysis to provide some evidence on the applicability of this method.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 28 (2012)
Issue (Month): 04 (August)
Pages: 838-860

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Handle: RePEc:cup:etheor:v:28:y:2012:i:04:p:838-860_00

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Cited by:
  1. Alessandro DE GREGORIO & Stefano Maria IACUS, 2011. "On a family of test statistics for discretely observed diffusion processes," Departmental Working Papers, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano 2011-37, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

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