A general class of small area estimation using calibrated hierarchical likelihood approach with applications to COVID-19 data

Nirosha Rathnayake, Hongying Daisy Dai, Richard Charnigo, Kendra Schmid, Jane Meza

Research output: Contribution to journalArticlepeer-review


The direct estimation techniques in small area estimation (SAE) models require sufficiently large sample sizes to provide accurate estimates. Hence, indirect model-based methodologies are developed to incorporate auxiliary information. The most commonly used SAE models, including the Fay-Herriot (FH) model and its extended models, are estimated using marginal likelihood estimation and the Bayesian methods, which rely heavily on the computationally intensive integration of likelihood function. In this article, we propose a Calibrated Hierarchical (CH) likelihood approach to obtain SAE through hierarchical estimation of fixed effects and random effects with the regression calibration method for bias correction. The latent random variables at the domain level are treated as ‘parameters’ and estimated jointly with other parameters of interest. Then the dispersion parameters are estimated iteratively based on the Laplace approximation of the profile likelihood. The proposed method avoids the intractable integration to estimate the marginal distribution. Hence, it can be applied to a wide class of distributions, including generalized linear mixed models, survival analysis, and joint modeling with distinct distributions. We demonstrate our method using an area-level analysis of publicly available count data from the novel coronavirus (COVID-19) positive cases.

Original languageEnglish
Pages (from-to)3384-3404
Number of pages21
JournalJournal of Applied Statistics
Issue number16
StatePublished - 2023

Bibliographical note

Funding Information:
This work was supported by Robert Wood Johnson Foundation: [Grant Number 76985]. We thank two referees and the Associate Editor for suggestions that led to substantial improvement of this paper. We acknowledge the Holland Computing Center of the University of Nebraska at Lincoln (HCC-UNL) for providing computing resources to conduct simulation studies.

Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.


  • COVID-19
  • Small area estimation
  • bias correction
  • hierarchical -likelihood

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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