Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series B, Pt. 1, 11-27

ROBUST MINIMUM DIVERGENCE PROCEDURES FOR COUNT DATA MODELS

By

AYANENDRANATH BASU,

SRABASHI BASU

And

GOPAL CHAUDHURI, Indian Statistical Institute

 

SUMMARY. Simpson (1987) considered minimum Hellinger distance estimation in count data models. Unlike many other robust estimators, the minimum Hellinger distance estimator is simultaneously robust and first order efficient. In particular Simpson provides appealing arguments for the robustness of the minimum Hellinger distance estimator, as well as attractive breakdown results for it. In particular Simpson provides appealing arguments for the robustness of the minimum Hellinger distance estimator, as well as attractive breakdown results for it. In this paper we show that Simpson's arguments for the Hellinger distance can be extended to a particular subclass of the Cressie-Read (Cressie and Read 1984) family of divergences where the corresponding estimators enjoy similar breakdown properties, and the estimating equations have a very simple weighted likelihood interpretation providing a nice diagnostic tool. The results of Lindsay (1994) provide further justification of the robustness of the estimators. Some numerical results are provided to illustrate the possible improvements in the performance of the estimators and the corresponding test statistics when an empty cell penalty is appropriately applied.

AMS (1991) subject classification. 62F35, 62F03, 62F10, 62F04

Key words and phrases. Hellinger distance, asymptotic efficiency, influence function, breakdown point, disparity, residual adjustment function, empty cells.

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