Statistica Sinica

Grace Y. Yi and Nancy Reid

Abstract:We consider the use of estimating functions that are not unbiased. Typically, to result in consistent estimators, unbiasedness of estimating functions is a pre-requisite. However, it is sometimes easier to find a useful estimating function that is biased, especially in the presence of missing data or misclassified observations. We show that the root of the estimating function can be modified to give a consistent and asymptotically normal estimator, and illustrate this on several examples with binary data. We compare this to the alternative approach of adjusting the estimating function, and show that it can be more efficient.

Key words and phrases:Binary data, bridge function, Godambe information, missing at random, misclassified.