Geodesic
Minimum disparity estimators for discrete and continuous models
Applications of Mathematics, Tome 46 (2001) no. 6, pp. 439-466

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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.
DOI : 10.1023/A:1013764612571
Classification : 62B10, 62E20
Keywords: divergence; disparity; minimum disparity estimators; robustness; asymptotic efficiency 
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Menéndez, M.; Morales, D.; Pardo, L.; Vajda, I. Minimum disparity estimators for discrete and continuous models. Applications of Mathematics, Tome 46 (2001) no. 6, pp. 439-466. doi: 10.1023/A:1013764612571

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