Since the core part of the framework above - the model specification and analysis - depends crucially on the problem to be solved and characteristics of available data, the literature for small area estimation is extensive. The following list, while by far not comprehensive, suggests books and guidelines that give a good introduction into the large variety of small area estimation methods, the different challenges and existing extensions.

Rao and Molina (2015). Small Area Estimation, New York: John Wiley & Sons.

The book is one of the most cited books in the field of small area estimation. It is an excellent reference for statisticians and practitioners that strive to learn small area estimation methodology.

It comprises methodology, practical applications and references to software.

Pratesi, M. (2016). Analysis of Poverty Data by Small Area Estimation, New York: John Wiley & Sons.

The book offers a comprehensive overview of how to use of SAE methods for poverty analysis with data from surveys and administrative archives. It covers, among others, the definition of poverty indicators, the impact of sampling design, weighting and variance estimation, and SAE modelling.

Bedi, T., Coudouel, A. and Simler, K. (2007). More Than a Pretty Picture : Using Poverty Maps to Design Better Policies and Interventions. Washington, DC: World Bank.
The book published by the  World Bank defines a poverty mapping process that was conducted in several countries. Based on surveys and additional data sources, various poverty and inequality estimates such as the Foster-Greer-Thorbecke poverty estimates and the Gini coefficient were derived.
ESSnet on Small Area Estimation (2012). Guidelines for the application of the small area estimation methods in NSI sample surveys. Eurostat.The guide aims to address the gap between survey sampling practices and the growing demand for disaggregated statistics. It provides standardized approaches to small area estimation based on existing sample survey data.
Asian Development Bank (2020). Introduction to Small Area Estimation techniques: A practical guide for national statistical offices. The guide is a nice introduction in basic small area estimation approaches with a special focus on the monitoring process of the SDGs. Furthermore, it gives an introduction to data management and the application of small area estimation methods in R.

Molina, I. (2019). Desagregación de datos en encuestas de hogares: metodologías de estimación en áreas pequeñas, CEPAL.

The collection is an excellent guideline for conducting analysis using small area estimation methods (in Spanish).
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