Orthogonal Locally Ancillary Estimating Functions with Application to Stratified Clustered Data

Abstract

We propose an orthogonal locally ancillary estimating function that provides first-order bias correction of inferences. It requires the specification of merely the first two moments of the observations when applying to analysis of stratified clustered (continuous or binary) data with the parameters of interest in both the first and second joint moments of dependent data. Simulation results confirm that the estimators obtained using the proposed method are substantially improved over those using regular profile estimating functions.

Keywords:

• Ancillarity
• Bias correction
• Clustered data
• Estimating function
• Nuisance parameter
• Orthogonality
• Sparse data

Mathematics Subject Classification:

• Primary 65F25

Acknowledgments

The authors would like to thank two referees for their helpful comments that improved the article.

Notes

Note: λ _i ws generated from Beta(μ_β, φ_β). Number of strata is 100. n is number of clusters in each stratum. Se _e , Se _b , and Se _a are empirical, bootstrap and analytical standard error, respectively.