 Optimal robust estimates using the Kullback-Leibler divergenceVictor J. Yohai Statistics & Probability Letters, 2008, vol. 78, issue 13, 1811-1816 Abstract: We define two measures of the performance of an estimating functional T of a multi-dimensional parameter, based on the Kullback-Leibler (KL) divergence. The first one is the KL sensitivity which measures the degree of robustness of the estimate under infinitesimal outlier contamination and the second one is the KL efficiency, which measures the asymptotic efficiency of the estimate based on T when the assumed model holds. Using these two measures we define optimal robust M-estimates using the Hampel approach. The optimal estimates are defined by maximizing the KL efficiency subject to a bound on the KL sensitivity. In this paper we show that these estimates coincide with the optimal estimates corresponding to another Hampel problem studied by Stahel [Stahel, W.A., 1981. Robust estimation, infinitesimal optimality and covariance matrix estimators. Ph.D. Thesis, ETH, Zurich]: to minimize the trace of a standardized asymptotic covariance matrix subject to a bound on the norm of a standardized gross error sensitivity, where both the asymptotic covariance matrix and the gross error sensitivity are standardized by means of the Fisher information matrix. Date: 2008 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:78:y:2008:i:13:p:1811-1816 Ordering information: This journal article can be ordered from Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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