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What would you guys suggest as a good introduction book to small area estimation?

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What resources have you collected so far? There can't even be that many "books" to choose from. The wikipedia article on small area estimation seems like a reasonable start. – Andy W May 10 '12 at 15:58
I've been there, I was just wondering if that's it. I mean I have found 2 books on the topic so far, that is not exactly what you would call a big repertoire to choose from... – user115032 May 10 '12 at 16:09
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It is a very recent field so yes that may be it. Besides the Rao book I would probably check out the two journal articles cited on wikipedia that appear to be reviews (one by Rao and one by Pfefferman). They likely have bibliographies of interest. Also just see who has cited the Rao book, not a tiny list, but reasonable to muck through for other reading of interest. Given its contemporary nature you may need to look into journal articles as well as books. – Andy W May 10 '12 at 16:17
I'd love to hear more about how this is or is not related to multi-level modeling. Seems like the idea is to borrow strength. – Wayne May 10 '12 at 17:41
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@AndyW, move this to an answer, I will +1 it. Because it is a comprehensive answer, in my opinion (of a survey statistician who has read most of the good SAE articles at some point). There were a couple of special issues of rather obscure journals (isas.org.in/jisas/jsp/onlinelatestissue.jsp, and another one that I cannot locate that followed the IASS meeting, stat.fi/isi99/iassscsae.html). But if you read Rao's book (and understand all of it), that will equip you fully with what you need to know to work in this area. – StasK May 11 '12 at 2:53

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It seems like the wikipedia article is a reasonable place to start. In particular, if you don't have access to the Rao book (which appears to be the only logical choice for a reference book), one might check out the two review articles cited on wikipedia as well;

It is a contemporary field, so any recent developments will more likely be contained within journal articles than books. One can utilize google scholar and the "cited by feature" to muck through anyone who has cited the Rao book. This in combination with just searching small area estimation is likely to yield a comprehensive list of popular literature on the subject.

If one wants to cast the net alittle bit broader, probably a natural extension to the multi-variate case is examining hierarchical spatial random effects models (Kang et al., 2009). Although these should come up in searches for "small area" anyway. There Noel Cressie's work will be of most interest, and many examples are currently in the public health/epidemiology although other examples in demography, sociology, economics and criminology exist as well (so examples are likely scattered a wide array of journals). I'm a social science guy so I'm ignorant to the extent such examples exist in the natural and environmental sciences. It also may be the case that one of Noel Cressie's book has topical material of interest, although I don't own any so I can't say for sure off-hand.

For completeness, the special issues Stask mentions in the comments;

While searching for any output of the IASS I came across some conferences in Europe entirely devoted to small area estimation, although they don't appear to have a devoted website (see examples for conferences in 2007, 2009, and 2011).

Also I noticed one statistician frequently particpating in those conferences that I had not mentioned so far was Partha Lahiri. Looking at his CV it looks like he is currently writing a book on small area estimation (as well as has a variety of other scholarly material of interest to the topic).

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