M. Menendez, Department of Applied Mathematics, Technical University of Madrid, Juan de Herrera 4, 28040 Madrid, Spain, e-mail: mmenende@aq.upm.es; D. Morales, Operations Research Center, Miguel Hernandez University of Elche, Elche, Spain, e-mail: d.morales@umh.es; L. Pardo, Department of Statistics and O. R., Complutense University of Madrid, Madrid, Spain, e-mail: Leandro_Pardo@mat.ucm.es; I. Vajda, Institute of Information Theory, Academy of Sciences of the Czech Republic, Prague, Czech Republic, e-mail: vajda@utia.cas.cz
Abstract: Disparities of discrete distributions are introduced as a natural and useful extension of the information-theoretic divergences. The minimum disparity point estimators are studied in regular discrete models with i.i.d. observations and their asymptotic efficiency of the first order, in the sense of Rao, is proved. These estimators are applied to continuous models with i.i.d. observations when the observation space is quantized by fixed points, or at random, by the sample quantiles of fixed orders. It is shown that the random quantization leads to estimators which are robust in the sense of Lindsay [9], and which can achieve the efficiency in the underlying continuous models provided these are regular enough.
Keywords: divergence, disparity, minimum disparity estimators, robustness, asymptotic efficiency
Classification (MSC 2000): 62B10, 62E20
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