Abstract
SummarySmall area estimation is a research area in official and survey statistics of great practical relevance for national statistical institutes and related organizations. Despite rapid developments in methodology and software, researchers and users would benefit from having practical guidelines for the process of small area estimation. We propose a general framework for the production of small area statistics that is governed by the principle of parsimony and is based on three broadly defined stages, namely specification, analysis and adaptation, and evaluation. Emphasis is given to the interaction between a user of small area statistics and the statistician in specifying the target geography and parameters in the light of the available data. Model-free and model-dependent methods are described with a focus on model selection and testing, model diagnostics and adaptations such as use of data transformations. Uncertainty measures and the use of model and design-based simulations for method evaluation are also at the centre of the paper. We illustrate the application of the proposed framework by using real data for the estimation of non-linear deprivation indicators. Linear statistics, e.g. averages, are included as special cases of the general framework.
Highlights
Small area estimation (SAE) has been and still predominately is a very fertile area of academic research in official statistics with important theoretical and applied contributions
In what sense can one set of estimates considered to be better than another? Is it enough that the underlying model is the preferred one according to some model selection criterion? Given two sets of ‘optimal’ estimates, derived under two different models, is it meaningful to compare the respective mean squared error (MSE) to each other directly? Is it enough that the average MSE of one set is better than the other? Should one rely on the design- or model-based MSE? Are ensemble properties of the small area estimates such as the range or ranks of the estimates relevant? These are all examples of questions, to which, in our opinion, there are hardly any definite answers
Notice that the conditional MSE is only applicable to an area that is present in the sample
Summary
Small area estimation (SAE) has been and still predominately is a very fertile area of academic research in official statistics with important theoretical and applied contributions. It is our view that the decision about which estimators to use should be governed by the principle of parsimony and we recommend that the Analysis and Adaptation stage start by using estimators that can be computed as part of the usual survey process within an NSI without involving explicit modelling or additional data sources These are the initial SAE estimates (see Section 3.1). For the purposes of empirical analysis in this paper we use a sample from the a household income and expenditure survey called ENIGH (Encuesta Nacional de Ingreso y Gasto de los Hogares) and a large sample of Census micro-data Both datasets are produced by the National Institute of Statistics and Geography (INEGI Instituto Nacional de Estadistica y Geografia) and they were provided to the authors by CONEVAL.
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