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INFERENCE

On Optimal Estimating Functions in the Presence of Nuisance Parameters

Pages 1867-1876 | Received 02 Apr 2004, Accepted 05 Oct 2006, Published online: 16 Jul 2007
 

Abstract

When there is only one interesting parameter θ1 and one nuisance parameter θ2, Godambe and Thompson (Citation1974) showed that the optimal estimating function for θ1 essentially is a linear function of the θ1-score, the square of the θ2-score, and the derivative of θ2-score with respect to θ2. Mukhopadhyay (2000b) generalized this result to m nuisance parameters. Mukhopadhyay (Citation2000 Citation2002a Citationb) obtained lower bounds to the variance of regular estimating functions in the presence of nuisance parameters. Taking cues from these results we propose a method of finding optimal estimating function for θ1 by taking the multiple regression equation on θ1 score and Bhattacharyya's (Citation1946) scores with respect to θ2. The result is extended to the case of m nuisance parameters.

Mathematics Subject Classification:

Acknowledgments

The author is grateful to the referee for some suggestions which helped improved the presentation of the article.

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