Parametric density estimation by minimizing nonextensive entropy

Davide Ferrari

Center for Economic Research (RECent) from University of Modena and Reggio E., Dept. of Economics "Marco Biagi"

Abstract: In this paper, we consider parametric density estimation based on minimizing the Havrda-Charvat-Tsallis nonextensive entropy. The resulting estimator, called the Maximum Lq-Likelihood estimator (MLqE), is indexed by a single distortion parameter q, which controls the trade-off between bias and variance. The method has two notable special cases. If q tends to 1, the MLqE is the Maximum Likelihood Estimator (MLE). When q = 1=2, the MLqE is a minimum Hellinger distance type of estimator with the perk of avoiding nonparametric techniques and the difficulties of bandwith selection. The MLqE is studied using asymptotic analysis, simulations and real-world data, showing that it conciliates two apparently contrasting needs: effciency and robustness, conditional to a proper choice of q. When the sample size is small or moderate, the MLqE trades bias for variance, resulting in a reduced mean squared error compared to the MLE. At the same time, the MLqE exhibits strong robustness at expense of a slightly reduced effciency in presence of observations discordant with the assumed model. To compute the MLq estimates, a fast and easy-to-implement algorithm based on a reweighting strategy is also supplied.

Keywords: Maximum Likelihood; q-Entropy; Robust Estimation (search for similar items in EconPapers)
Pages: pages 39
Date: 2008-05
New Economics Papers: this item is included in nep-ecm
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://155.185.68.2/campusone/web_dep/Recentpaper/recent-wp16.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 404 Not Found

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:mod:recent:016

Access Statistics for this paper

More papers in Center for Economic Research (RECent) from University of Modena and Reggio E., Dept. of Economics "Marco Biagi" Contact information at EDIRC.
Bibliographic data for series maintained by ().