In Chapter 4 of Lohr, S.L.(2010), Sampling: Design and Analysis, 2nd ed., Brooks/Cole, she explains the design-based and model-based CRE. On pages 158-160 of Cochran, W.G.(1977), Sampling Techniques, 3rd ed., John Wiley & Sons, he also briefly discusses the model-based CRE, amidst his discussion of the design-based CRE. The model-based format can further be found in other contexts in econometrics books. The attached links provide more information and usage. Cochran, page 160, noted that (under what seem mild conditions) it could be "hard to beat."
Where and how have you used the model-based classical ratio estimator, or might you have seen it used?
https://www.researchgate.net/publication/261474011_The_Classical_Ratio_Estimator_%28Model-Based%29
https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements
Article The Classical Ratio Estimator (Model-Based)
Conference Paper Projected Variance for the Model-based Classical Ratio Estim...
I have not used it by try this link to see if it will be useful to you.
http://interstat.statjournals.net/YEAR/2012/articles/1209001.pdf http://interstat.statjournals.net/YEAR/2012/articles/1205002.pdf
Besides Sharon Lohr's comments in her survey analysis book, and other survey statistics books, I have seen the CRE appear in different author's econometrics books. It seems that it might usually be the example they employ to show how to transform to "remove" heteroscedasticity for hypothesis testing (with which I disagree, BTW - please see attached). In Maddala's last book (with Lahiri) they did an example showing heteroscedasticity measured in a way in which they picked one of several alternatives for that example as looking closest to truth. The one they picked, in that example, was for the degree of heteroscedasticity in the CRE.
So I would expect that there are some econometricians, survey statisticians, and others who have had some experience with this. Though econometric models are generally much more complex, I would think this would be a part of them.
Any comments?
(I had wanted to refrain from answering my own question, but I hope that this will generate some comments from others.)
Article Practical Interpretation of Hypothesis Tests - letter to the...
Model approache in the case of the ratio estimators is considered by Chaudhuri A., Stenger H. (2005). Survey Sampling. Theory and Methods.
Chapman & Hall/CRC Taylor & Francis Group, Boca Raton, London,
New York, Singapore.
Please consider the formulation below for weighted least squares (WLS) simple linear regression through the origin, from pages 7 and 8 of the paper to be found through use of the attached link. When we can use gamma=1/2, we have the CRE, which may be robust though gamma may be estimated to be larger for given applications. (Gamma is the coefficient of heteroscedasticity.)
Considering the additional reference to G.S. Maddala here, might that be a reminder of an application of the CRE you may have seen?
Article Quasi-Cutoff Sampling and Simple Small Area Estimation with ...
Sorry. It seems ResearchGate keeps losing the two attachments on my original question. In case that happens again, I attach those links here too.
Thank You.
https://www.researchgate.net/publication/261474011_The_Classical_Ratio_Estimator_%28Model-Based%29
https://www.researchgate.net/publication/261947825_Projected_Variance_for_the_Model-based_Classical_Ratio_Estimator_Estimating_Sample_Size_Requirements
Article The Classical Ratio Estimator (Model-Based)
Conference Paper Projected Variance for the Model-based Classical Ratio Estim...
Apparently when I tried to "share" this question with many of my contacts on ResearchGate, the message was delivered without giving the link. If you found your way here anyway, thank you, and I apologize for the inconvenience. To those who did not find this, I wish I could apologize now. But I may try sending it again later, although that will be a repeated message similar to the one ResearchGate dropped, so I will at least wait a while to give them a chance to fix the 'bugs' in their software.
Dear James et al,
Your question is so important in econometrics that i must read your papers before i answer it.
It is a must and i should do this because i really respect science and i need to learn from others like you.
I hope very soon to answer your question.
.Thank you for sharing your knowledge.
Have a nice day
Helena
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