Try some of Pierre Gy's texts from 1953 onwards..... They relate to sampling of particulate materials but contain extensive statistical modeling. "Sampling of Particulate Materials" from 1979 was based on earlier texts in French.  Not being a lecturer and writing in French was a disadvantage.... One can go back to the 1880's for early work in this area.  See for example:

December 9th, 2013 Sylvanus Albert Reed and sampling theories in the 1880’s

https://www.brainshark.com/malvern/vu?pi=285211271&text=M021507

Alan, and all - 

The link you attached provided an interesting portrait of a very versatile person. 

As for particulate sampling, that not being familiar to me, I did an Internet search, and it seemed that two varieties of heterogeneity were considered, but I don't know the connection to survey sampling, say establishment or household or agricultural surveys, relevant to Cochran.  One confusion may be that the word "model" associated with ore sampling may be far different than the regression models referred to by Cochran.  However, I do recall a mineral assay problem, I think, used as a example in Carroll and Ruppert(1988), Transformation and Weighting in Regression, Chapman & Hall, Ltd. London, UK.  

So, I'm not clear as to whether or not the work you note by Pierre Gy, and Sylvanus Albert Reed, which I think I saw somewhere may relate to agricultural crops (though I may have that wrong), might or might not relate to the kind of finite population sampling in such books as the following, where I am interested in the use of regression (model) 'prediction,' rather than only randomized sampling where only selection probabilities are used for estimation:

Cochran, W.G(1977), Sampling Techniques, 3rd ed., John Wiley & Sons. 

Blair, E. and Blair, J(2015), Applied Survey Sampling, Sage Publications.

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.     

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

I find cross-fertilization among fields useful and interesting.  When I've attended the Joint Statistical Meetings, sponsored by several organizations, including the American Statistical Association, I have found it interesting to attend sessions not in my area and especially for subject matters not familiar to me.  It seems that different disciplines may develop similar statistical concepts under different terminology, and perhaps different concepts with similar terminology.  I am also reminded of a biological term I've heard, "parallel evolution." 

If you could tell us what "model" means in your field, that would be edifying.   -  Thank you.

Cheers - Jim

Hi Jim Thanks for your detailed and thoughtful reply.  I realized that the link was somewhat tenuous but does relate to heterogeneity of samples and distributions (in this case, particle size distributions).  Yes, you're right it does get down to what we mean by 'model'.  We could lump in Student's T-Test (another interesting guy - an Irish Mathematician in Guinness....) or Pearson's Rank Correlation.  Or Poisson.... I guess model and algorithm aren't really synonymous.  However, all are models of some perceived universal 'truth' (if the entre population could be sampled). And we know that 'In theory, theory and practice agree. In practice, they do not'.  There were a bunch of early particle sizing sampling experts around and I find it fascinating all of the fields they were involved in.  Consider:

December 13th, 2012 David W Brunton and sampling theories in the late 1800's

https://www.brainshark.com/malvern/vu?pi=181297280&text=M021507

December 16th, 2013 Robert Hallowell Richards, his wife Ellen Swallow Richards, and sampling theories in the 1900 – 1910 period

https://www.brainshark.com/malvern/vu?pi=192277776&text=M021507

December 9th, 2015 Philip Argall and early sampling practice in Colorado

https://www.brainshark.com/malvern/vu?pi=941720380&b=1&tx=120486&c1=22

In terms of what you state about different terms in different fields, I concur.  It was quite sometime before I realized that Gy's "Fundamental Sampling Error" (FSE) was identical to the 'standard error' that I'd been taught in my university text books:

- C J Brookes, I G Betteley, A M Loxston “Mathematics and Statistics for Chemists” John Wiley & Sons page 266  (1966)

- Harold Lucas “Statistical Methods” Butterworths page 77 (1970)

 BTW, I do a yearly sampling for particle size course at Pittcon each year - it's 1/2 day.  That's where my (sampling) interest is channeled!

And I did forget perhaps the greatest exponent of theory and practice, Henry Vezin:

September 4th, 2014 Henry Vezin and early sampling practice (1850's - 1900)

http://tinyurl.com/njahy8c

Thanks Alan. 

Anyone have anything on regression models used in mid- to late-20th century survey sampling textbooks, in addition to Cochran's Sampling Techniques, or more on Cochran?   Thank you.  (Morris Hansen did  not like models and balked when Ken Brewer brought them up.  Ken used them for various purposes including early use to help decide on the best random sampling design.  Ken wrote many articles, but his reference book wasn't published until 2002.  Särndal, Swensson, and Wretman was 1992, but anything else earlier?) 

Another book that comes to mind is Sampling Theory (1968) by Des Raj. 

And definitely,

Design and Inference in Finite Population Sampling (Wiley Series in Survey Methodology) 1st Edition (1992) by Hedayat and Sinha

and

Foundations of Inference in Survey Sampling 1st Edition (1977)

by Claes Cassel, Carl-Erik Sarndal, Jan Hakan Wretman 

Ah.  Thanks Samson.  I do remember seeing the third book now, Foundations, but recall no specifics about it.  Don't think I was ever acquainted with the other two books.  Good hearing about them also.  Thanks.  So when I think that Morris Hansen told Ken Brewer 'we don't need models,' it seems that it wasn't just Royall and one or two others with whom he was disagreeing. 

Dear Prof.James R Knaub

My Heartiest Greetings!

The other books deal with models in sampling are:

M.N. Murthy- Sampling - Theory and Methods, 1967

HAJEK J - Sampling from finite populations- 1981

I hope it will be useful.

JS

Thank you Prof. Subramani.  I appreciate your contribution.  This is very helpful. 

- (no Dr., Prof.) Jim Knaub

Thanks for the contributions. 

To summarize thus far, survey sampling textbooks of the 20th Century which included use of models were as follows:

Cochran, W.G(1953, 1963?, 1977), Sampling Techniques, three editions, John Wiley & Sons.

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

Sampling Theory (1968) by Des Raj. 

Design and Inference in Finite Population Sampling (Wiley Series in Survey Methodology) 1st Edition (1992) by Hedayat and Sinha

Foundations of Inference in Survey Sampling 1st Edition (1977), by Claes Cassel, Carl-Erik Sarndal, Jan Hakan Wretman 

M.N. Murthy- Sampling - Theory and Methods, 1967

HAJEK J - Sampling from finite populations- 1981

...

Further, the following book which combines design-based and model-based sampling and estimation just missed this 20th century "deadline" by two years:

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

But Ken Brewer had perhaps what could be considered the first modern use of regression models in survey sampling in an article referenced in Cochran(1977):

 Brewer, K.R.W. (1963), "Ratio Estimation in Finite Populations: Some Results Deducible from the Assumption of an Underlying Stochastic Process," Australian Journal of Statistics, 5, pp. 93-105,

followed by

 Royall, R.M. (1970), "On Finite Population Sampling Theory Under Certain Linear Regression Models," Biometrika, 57, pp. 377-387.

(There is reference, even in Cochran, to work in agriculture in an article by H. Fairfield Smith in 1938, which led to weighted least squares regression.) 

...

There are perhaps many 21st century books besides Brewer(2002) which cover regression modeling to some extent. 

Lohr, S.L(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole, does a particularly good job of comparing the design-based classical ratio to the model-based classical ratio estimator  (CRE).  

Here are 21st century (if you count year 2000) textbooks I have, which concentrate on "prediction" (i.e., regression modeling):

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. 

...

But, back to the history of the 20th and 21st centuries, and earlier, in Ken Brewer's Waksberg Award article: 

In Brewer, K.R.W. (2014), “Three controversies in the history of survey sampling,” Survey Methodology,

(December 2013/January 2014), Vol 39, No 2, pp. 249-262. Statistics Canada, Catalogue No. 12-001-X.

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

we see that Ken argues, especially for intermediate sized samples, for using probability sampling and models together.  He explains the different approaches, the pros and cons. 

In that article he gives some history, back to the 19th century, and I know the following article to be entertaining:

Brewer, K.R.W. (2005). Anomalies, probings, insights: Ken Foreman's role in the sampling inference controversy of the late 20th century. Australian and New Zealand Journal of Statistics, 47, 4, 385-399. 

...

...

So, I had asked this question in order to compose a list of the use of models in survey sampling textbooks in the latter 20th century because that is when the use of models for survey statistics was perhaps least in favor.  In the distant past (say maybe 17th century or perhaps earlier), and in modern survey statistics, the use of models is far more popular.  (I have seen, for example, where Anders Holmberg, in 2007, extended to multiple dependent variables, the use Ken Brewer made of models to aid in design-based sampling and estimation for unequal probability sampling, in 1963, a big year for Ken, in my opinion.)   And in virtually every other area of statistics, models are used extensively.  And though there is great use of models in modern survey statistics, there are some who, for pholosophical reasons, decline their use, and ignore the shortcomings and potentially extremely 'unrepresentative' nature of randomized sampling, to concentrate on randomized sampling only.   There is good reason to consider regression models, at least as an aid.  In some finite population cases, say highly skewed establishment surveys, they are more important.  

I thought that a list of survey sampling textbooks making mention of regression models in any way, at a time (the latter half of the 20th century) when generally only articles/papers on survey sampling made any use of models, would be rather short (with much greater use in other areas of statistics), but as noted above, with thanks to help from Samson Adeshiyan, and Jambulingam Subramani, there are at least seven such survey sampling textbooks:

Cochran, W.G(1953, 1963?, 1977), Sampling Techniques, three editions, John Wiley & Sons.   

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

Sampling Theory (1968) by Des Raj. 

Design and Inference in Finite Population Sampling (Wiley Series in Survey Methodology) 1st Edition (1992) by Hedayat and Sinha

Foundations of Inference in Survey Sampling 1st Edition (1977), by Claes Cassel, Carl-Erik Sarndal, Jan Hakan Wretman 

M.N. Murthy- Sampling - Theory and Methods, 1967

HAJEK J - Sampling from finite populations- 1981

...

Two more just missed the 1900s, as also noted above:

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

Richard Valliant, Alan H. Dorfman, Richard M. Royall, Wiley Series in Probability and Statistics. 

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

...

Any more? 

Thank you. 

A related thread: 

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

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