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ADAPTIVE LASSO-TYPE ESTIMATION FOR MULTIVARIATE DIFFUSION PROCESSES

Published online by Cambridge University Press:  21 February 2012

Alessandro De Gregorio  and
Stefano M. Iacus
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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.

Type
Research Article
Information
Econometric Theory , Volume 28 , Issue 4 , August 2012 , pp. 838 - 860
Copyright
Copyright © Cambridge University Press 2012

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Footnotes

The authors would like to thank the editor and two anonymous referees for their comments and suggestions, which led to a substantial improvement of the earlier versions of the manuscript.

References

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