MLE with datasets from populations having shared parameters

Abstract

We consider maximum likelihood estimation with two or more datasets sampled from different populations with shared parameters. Although more datasets with shared parameters can increase statistical accuracy, this paper shows how to handle heterogeneity among different populations for correctness of estimation and inference. Asymptotic distributions of maximum likelihood estimators are derived under either regular cases where regularity conditions are satisfied or some non-regular situations. A bootstrap variance estimator for assessing performance of estimators and/or making large sample inference is also introduced and evaluated in a simulation study.

Keywords:

• Accuracy
• asymptotic relative efficiency
• bootstrap
• population heterogeneity
• regularity conditions

Acknowledgments

The authors would like to thank two anonymous referees for helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Jun Shao's research was partially supported by the National Natural Science Foundation of China [Grant Number 11831008] and the U.S. National Science Foundation [Grant Number DMS-1914411].