A resampling approach to estimation of the linking variance in the Fay–Herriot model

ABSTRACT

In the Fay–Herriot model, we consider estimators of the linking variance obtained using different types of resampling schemes. The usefulness of this approach is that even when the estimator from the original data falls below zero or any other specified threshold, several of the resamples can potentially yield values above the threshold. We establish asymptotic consistency of the resampling-based estimator of the linking variance for a wide variety of resampling schemes and show the efficacy of using the proposed approach in numeric examples.

KEYWORDS:

• Linking variance
• Prasad–Rao estimator
• paired bootstrap
• m-out-of-n bootstrap
• Bayesian bootstrap

Acknowledgments

The author thanks the reviewers and editors for their comments, which helped improve the paper.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Snigdhansu Chatterjee http://orcid.org/0000-0002-7986-0470

Additional information

Funding

This research is partially supported by the National Science Foundation (NSF) [grant numbers # DMS-1622483 and # DMS-1737918].

Notes on contributors

Snigdhansu Chatterjee

Dr. Snigdhansu Chatterjee is Professor in the School of Statistics, and the Director of the Institute for Research in Statistics and its Applications (IRSA, http://irsa.stat.umn.edu/) at the University of Minnesota.