Robust Small Area Estimation : Methods, Theory, Applications, and Open Problems

In recent years there has been substantial and growing interest in small area estimation (SAE) that is largely driven by practical demands. Here, the term "small area" typically refers to a subpopulation or domain of interest for which a reliable direct estimate, based only on the domain-specific sample, cannot be produced due to small sample size in the domain.

Keywords in SAE are “borrowing strength”. Because there are insufficient samples from the small areas to produce reliable direct estimates, statistical methods are sought to utilize other sources of information to do better than the direct estimates. A typical way of borrowing strength is via statistical modelling. On the other hand, there is no “free lunch”. Yes, one can do better by borrowing strength, but there is a cost. This is the main topic discussed in this text.

Features

• A comprehensive account of methods, applications, as well as some open problems related to robust SAE
• Methods illustrated by worked examples and case studies using real data
• Discusses some advanced topics including benchmarking, Bayesian approaches, machine learning methods, missing data, and classified mixed model prediction
• Supplemented with code and data via a website

Robust Small Area Estimation: Methods, Applications, and Open Problems is primarily aimed at researchers and graduate students of statistics and data science and would also be suitable for geography and survey methodology researchers. The practical approach should help persuade practitioners, such as those in government agencies, to more readily adopt robust SAE methods. It could be used to teach a graduate-level course to students with a background in mathematical statistics.

Jiming Jiang is a Professor of Statistics and Chair of the Department of Statistics at the University of California, Davis. His research interests include mixed effects models, small area estimation, model selection, statistical genetics/bioinformatics, and asymptotic theory. He is author of over 100 peer-reviewed publications and six books/monographs, including Linear and Generalized Linear Mixed Models and Their Applications (Springer 2007, 2nd ed. 2021), Large Sample Techniques for Statistics (Springer 2010, 2nd ed. 2022), The Fence Methods (World Scientific 2015; joint with Nguyen), Asymptotic Analysis of Mixed Effects Models: Theory, Application, and Open Problems (Chapman & Hall/CRC, 2017), Robust Mixed Model Analysis (World Scientific 2019), and Robust Small Area Estimation: Methods, Theory, Applications and Open Problems (Chapman & Hall/CRC, 2025; joint with Rao). He has served editorial boards of several major statistical journals including the Annals of Statistics and Journal of the American Statistical Association. He is a Fellow of the American Association for the Advancement of Science, a Fellow of the American Statistical Association (ASA), a Fellow of the Institute of Mathematical Statistics, and an Elected Member of the International Statistical Institute. He is a co-recipient of Outstanding Statistical Application Award (ASA, 1998), a (first) co-recipient of Distinguished Alumni Award (National Institute of Statistical Sciences, 2015), a Yangtze River Scholar (Chaired Professor, 2017-2020), a Primary Speaker of the Morris Hansen Lecture (Washington Statistical Society, 2023), and a recipient of the Award for Outstanding Contribution to Small Area Estimation (the SAE Award, 2024).

J. Sunil Rao is Professor in the Division of Biostatistics and Health Data Science at the University of Minnesota, Twin Cities. He is also the Director of Biostatistics at the Masonic Cancer Center and Founding Chair and Professor Emeritus in the Division of Biostatistics at the University of Miami. His research interests include mixed modelling, small area estimation, high dimensional data analysis, modelling of cancer genomic data and statistical methods for health disparity research. He is author of over 100 peer-reviewed publications and two books/monographs, including Statistical Methods in Health Disparity Research (Chapman & Hall/CRC, 2023) and Robust Small Area Estimation: Methods, Theory, Applications and Open Problems (Chapman & Hall/CRC, 2025; joint with Jiang). He is Fellow of the American Statistical Association, Fellow of the Institute of Mathematical Statistics and an Elected Member of the International Statistical Institute. He has served as an Associate Editor for a number of different statistical journals. He received the V.K. Gupta Endowment Award for Achievements in Statistical Thinking and Practice (2024) and was appointed as an Honorary Member of the Society for Statistics, Computers and Applications (2024).