I usually use Cochran, W.G (1977) for sampling techniques and methods. I think it is one of the best statistics textbooks in this subject.

Dear James

I use Cochran (1977),

Kish, Leslie (1965), Survey Sampling,

Des Raj (1968) Sampling Theory, Särndal, CE, Swensson, B. and Wretman, J. (1992), 

Lohr, S.L(2010),

Ruiz Espejo (1913) Exactitud de la Inferencia en Poblaciones Finitas.

I hope this help

Thank you to participants thus far. 

I am looking to see what various books say about design-based (probability of selection) compared to model-based (prediction) ratio estimation, and it occurred to me that there is another book, of which I own a copy, I thought might do that:

Survey Sampling: Theory and Methods, First Edition, 1992,

Chaudhuri, A., and Stenger, H.,

Marcel Dekker, lnc.

There was a second edition by CRC Press about a decade later, but I don't have that one. 

I checked and noticed what appears to be interesting discussions that might be quickly labeled design-based, perhaps starting around page 55,  and model-based, perhaps starting around page 74 forward. 

..............................

.

What I really want to know is what textbooks, besides this one and those I listed in my question explanation, cover both design-based and model-based ratio estimation, especially the classical ratio estimator  (CRE). 

Thank you.

Have you checked Valliant, Dorfman and Royall (2000)? Also Chambers, Steel, Wang and Welsh (2012) may have some information. I have an extra copy of the latter that I can send your way.

Dear James 

I am reading Rao (2003), "Small Area Estimation" Wiley, which covers this matters.

I hope this help you.

Guillermo

Thank you both, Stanislav and Guillermo, I do own both a copy of the (1) Valliant, Dorfman and Royall (2000), prediction approach to finite populations book, and the (2) Rao & Molina(2015) - i.e., next edition of Rao small area estimation book.  I'm in the process of checking a number of textbooks. 

Right now I own a number of books, some I got from recommendations from ResearchGate folks, and I have been seeing what the same author has to say about both model-based and design-based approaches to ratio estimation.  I had written a paper or two before, which talked about the way people look at this estimation, both in theory and in my experience, and there is another paper i wrote recently where I compared the two variance estimators, showing how they relate to each other/under what conditions, and now I'm reviewing that and have done a lot of research on what others thought and did, and when. 

Ken Brewer was also interested in these kinds of historical perspectives, and wrote a paper once on his experiences, with Ken Foreman as a mentor, that had some humor.   He (Ken Brewer) also wrote this:

 http://www.statcan.gc.ca/pub/12-001-x/2013002/article/11883-eng.htm

It suddenly occurs to me that that Waksberg paper of his, which talked about the history of design-based and model-based methods, and his work combining them, relates greatly to what I'm doing.  I am looking, in a way, at a more narrow aspect of design-based related to model-based theory and practice, and because of Ken's influence, I have become more interested in history.  The interest in history just seemed to have slipped in there! 

This leads to the book I found by Deming, from 1950, Some Theory of Sampling, which references Deming's book from 1938/1943-"corrected" in 1964, Statistical Adjustment of Data.  In Some Theory of Sampling, after saying the book deals "entirely" with probability samples, and talking about a design-based approach to the classical ratio estimator, he has an entire chapter on the study on which he published a paper with Jessen, Blythe, and Kempthorne in JASA 1947, regarding the postwar population in Greece.  That paper famously used what Särndal, Swensson and Wretman (1992), Model Assisted Survey Sampling, would call an 'alternative' ratio estimator, with greater heteroscedasticity.  (The degree of heteroscedasticity there is only slightly larger than what is routinely found by measurement of most establishment survey cases in practice.  However, I have found that the classical ratio estimator can be more robust in a 'production' environment for official statistics.)  Anyway, Deming noted the model-based (though I don't see where he called it that, and he still used random sampling apparently) and design-based methods regarding ratios, but actually looked at the design-based method differently enough that he, as in Hansen, Hurwitz and Maddow (1953), reversed the roles of x and y in the formulation there!  For the Greek population case, he used x and y as you would in a regression model, and also used this to make what really amounts to an approximate model-based prediction interval that made the cover of the book! 

Anyway, I appreciate the references.  And Guillermo, I did pick up a copy of Des Raj, as you suggested earlier.  Thank you.  -  Others on another question gave me book references, and I appreciate that too:

 https://www.researchgate.net/post/In_addition_to_Cochrans_Sampling_Techniques_what_other_survey_sampling_text_of_that_period_made_use_of_models/1

Thank you all.  -   Jim 

PS - Guillermo, I had not thought that the Rao book would fit into my current study, but as you, and I think someone else suggested it, I now intend to include a search there too. Thank you.

Note that the 2003 edition of Rao (without Molina) did have the material on ratio estimation, but it was taken out of the 2015 second edition. So you really need to have both, I guess.

Ah!  Thanks for the 'heads up.'  I may look for a used copy, but I have a great deal of material now, from rather old to quite new, and may not get to that.  - Thanks. 

..... 

PS -  Found one for about $18 including shipping, so I just ordered it.   :-)  

Thank you both -

and thanks to all.   

I do no know if you have seen, "Advanced Sampling Theory with Applications: How Michael Selected Amy", if not see some detail is here:

http://www.springer.com/us/book/9781402016899#aboutBook

Let me add something a bit more:  One day the following monograph will be on the lips of every survey statistician:

A new concept for tuning design weights in survey sampling: Jackknifing in Theory and Practice. Elsevier (2015).

https://www.amazon.com/Concept-Tuning-Design-Weights-Sampling/dp/0081005946/ref=sr_1_1?ie=UTF8&qid=1497659688&sr=8-1&keywords=sarjinder

After this new concept, you do not need anything else!  It is a almost dead end of survey sampling!    After this, new research, if you are coming to the JSM-2017, please visit my booth "STAT-HAWKERS" or come to my talk:

https://ww2.amstat.org/meetings/jsm/2017/onlineprogram/AbstractDetails.cfm?abstractid=323636

Hope to see you there!

Yes, I have heard of Michael/Amy.    Does it include model-assisted design-based and strictly model-based methodology/inference (as opposed to strictly design-based), such as found in varying degrees among the following, for example? 

Brewer, KRW (2002), Combined survey sampling inference: Weighing Basu's elephants, Arnold: London and Oxford University Press.  

An Introduction to Model-Based Survey Sampling with Applications, 2012,

Ray Chambers and Robert Clark,  Oxford Statistical Science Series

Finite Population Sampling and Inference: A Prediction Approach,  2000,

Richard Valliant, Alan H. Dorfman, Richard M. Royall,

Wiley Series in Probability and Statistics

Thompson, S.K.(2012), Sampling, 3rd ed, John Wiley & Sons.

Lohr, S.L(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole.

Särndal, CE, Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling, Springer-Verlang.   

.....

As for the jackknife and calibration, they can often be useful.  But I'd caution every time that anyone implies that to too large of a degree "one size [or methodology] fits all" situations. 

Proverb: "If all you have is a hammer, then every problem looks like a nail."

Cochran, W.G (1977)

Relevant paper:

I am posting the following to this Q&A thread, and also to one other, both URLs given below. 

In August 2017, I presented a poster paper, "Comparison of Model-Based to Design-Based Ratio Estimators" to the Joint Statistical Meetings (JSM):

 https://www.researchgate.net/publication/319434665_Comparison_of_Model-Based_to_Design-Based_Ratio_Estimators

Note the link to the extensive bibliography given on the last page.

Further, in the acknowledgements there is this:

"Also, thank you to those researchers on ResearchGate who answered my requests for suggestions for more textbooks to consult."

https://www.researchgate.net/post/In_addition_to_Cochrans_Sampling_Techniques_what_other_survey_sampling_text_of_that_period_made_use_of_models

https://www.researchgate.net/post/What_statistics_textbooks_do_you_know_which_do_a_good_job_of_covering_both_the_design-based_and_the_model-based_classical_ratio_estimator_CRE