ROBUST INFERENCE IN PARAMETRIC MODELS USING THE FAMILY OF GENERALIZED NEGATIVE EXPONENTIAL DISPARITIES

Autor:	Ayanendranath Basu, Subir Kumar Bhandari, Sahadeb Sarkar
Rok vydání:	2006
Předmět:	Statistics and Probability Likelihood-ratio test Statistics Parametric model Estimator Inference Deviance (statistics) Statistics Probability and Uncertainty Hellinger distance Null hypothesis Negative exponential Mathematics
Zdroj:	Australian New Zealand Journal of Statistics. 48:95-114
ISSN:	1467-842X 1369-1473
DOI:	10.1111/j.1467-842x.2006.00428.x
Popis:	Summary We examine robust estimators and tests using the family of generalized negative exponential disparities, which contains the Pearson's chi-square and the ordinary negative exponential disparity as special cases. The influence function and α-influence function of the proposed estimators are discussed and their breakdown points derived. Under the model, the estimators are asymptotically efficient, and are shown to have an asymptotic breakdown point of 50%. The proposed tests are shown to be equivalent to the likelihood ratio test under the null hypothesis, and their breakdown points are obtained. The competitive performance of the proposed estimators and tests relative to those based on the Hellinger distance is illustrated through examples and simulation results. Unlike the Hellinger distance, several members of this family of generalized negative exponential disparities generate estimators which also possess excellent inlier-controlling capability. The corresponding tests of hypothesis are shown to have better power breakdown than the Hellinger deviance test in the cases examined.
Databáze:	OpenAIRE
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