Dear Jim, if I may,

Roughly, small area estimation is one of the statistical techniques (including the estimation of parameters for sub-populations), used when the sub-population in question is integrated in a larger context.

I tend to agree with you. SAE doesn't refer to any specific technique or estimation philosophy. But I would add to your definition the obvious proviso that there is insufficient data for design based estimation at the required level and precision. If design based estimators have insufficient accuracy then either we have to give up or make some modelling assumptions. All models gather strength from somehwere, Bayesian models get it from prior beliefs, but more often it comes from some sort of smoothness assumption--we expect similar units to have similar behaviour.

I also tend to agree with you - we used the 'borrowing strength' inherent in the multilevel model in these papers

https://www.researchgate.net/publication/12600791_Predicting_small-area_health-related_behaviour_a_comparison_of_smoking_and_drinking_indicators

https://www.researchgate.net/publication/23539627_Developing_and_evaluating_small-area_indicators_of_the_neighbourhood_social_environment

and it worked rather well according to this evaluation

https://www.researchgate.net/publication/11374674_Predicting_small_area_health-related_behaviour_a_comparison_of_multilevel_synthetic_estimation_and_local_survey_data

Article Predicting small-area health-related behaviour: a comparison...

Article Developing and evaluating small-area indicators of the neigh...

Article Predicting small area health-related behaviour: A comparison...

Dear Jim, if I may,

Roughly, small area estimation is one of the statistical techniques (including the estimation of parameters for sub-populations), used when the sub-population in question is integrated in a larger context.

I tend to agree with my friend Marwan. Small area means a small geographical expanse as county or district. It may also refer to a population in such a geographical small unit. In a survey, the sample size within a small area cannot be generalised for the bigger area constituted by small areas. Therefore, it involves the estimation of parameters for small sub-populations, generally used when the sub-population of interest is included in a larger survey. There is no single standard for small area estimation for finite population rather several statistical techniques. One of the more common small area models in use today is the 'nested area unit level regression model'.

Hopefully you will not understand anything from the references cited here!  Most of the research articles are written in such a way that only a group of people can understand these papers or books or monographs.   I have full rack of monographs. I cite these monographs to publish my work, but I could not understand anything from them. Old textbooks like Cochran (1963), Sukhatme, Sukhatme and Asok(1984) and  Murthy (1964)  are good one.  Look for Domain Estimation and you will get an idea. Look for Hidden Gangs in finite populations, that is also a kind of domain estimation!  I hope it will help!

Census

• Population of interest (or target population): population for which the survey is designed - direct estimators; should be reliable for the target population
• Domain: sub-population of the population of interest, they could be planned or not in the survey design
• Geographic areas (e.g. Regions, Provinces, Municipalities, Health Service Area)

Consider 'synthetic estimation' for high 'coverage,' nonprobability sampling of continuous data, with the finite population properly divided* by model application, and smaller 'areas' are to be found within each division. Does this meet your minimally acceptable definition of "small area estimation," that estimation be accomplished with the help of "borrowed" data?

*[I have thought of this as a kind of 'stratification,' but stratification is done to improve overall estimates, whereas here we want to do the opposite: we want to publish within the lower, pseudo-stratum level. It is something like the reverse of stratification. Instead of several models, one for each stratum, to obtain a better overall estimate, here we have data such that one model for a given larger 'area' is used to estimate for smaller areas within it.]

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One could think of this as imputation for nonresponse to a census. As long as each model application is confined to data that follow that model, as determined by scatterplots and other testing, ignorability is being considered. The estimated variance of the prediction errors for estimated totals for each 'small area' will generally not be acceptably low without high 'coverage' for each such small area, but it is that variance estimate that matters.

With that background, is "borrowing strength," as in the article found through the attached link, sufficient to refer to this as "small area estimation"? Comments please. 

Article Quasi-Cutoff Sampling and Simple Small Area Estimation with ...

Notice:  

I am now going to submit the last part above as a separate question on RG, regarding that article.  I invite your comments there, wherever RG lets me post the question.   -  

Thank you.  -  Jim 

The figure here, found in  http://www.amstat.org/sections/SRMS/Proceedings/papers/1999_115.pdf ,  is one example from Official Statistics where it may seem that the smaller respondents are behaving differently than the others (and actually they are), but it is a matter of modeling data in the right groupings. The US Pacific Contiguous Census Division is an aggregate level being reported for California, Oregon and Washington combined (CA, OR, WA), and separately by small area estimation, but CA does not model well with OR and WA for hydroelectric generation. It is better to model the US National Climatic Data Center (NOAA's NCDC) regions involved: (1) CA & NV , (2) OR , WA, & ID.