Horvitz, D. G. and Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association 47, 663–685. MR0053460
The above paper by Horvitz and Thompson (1952) seems backbone of complex designs in survey sampling.
At the same time, I have never seen any paper either by Prof. D.G. Horvitz, or by Prof. D. J. Thompson, or by both on the same 1952 work.
If the authors never promoted (or used) their work, then why other Survey Statisticians are making the HT-estimator so much popular?
Is there any reason (or a story) behind it? Am I missing some work by them?
Hi,
This is not question, please read the question again. The question is other survey statistician as you mentioned a few here always work on it, and claiming they are doing a great job, but the pioneer authors' (H and T) never worked on it? Why?
Regards,
Sarjinder
@ Dr. Dey: GREG is model unbiased. My work TRUMP that is Tuned Ratio Unbiased Mean Predictor as well as Tuned Regression Unbiased Mean Predictors are also model unbiased.
@Dey: For some designs, the ratio estimator as sell as linear regression estimators also design unbiased. Follow Advanced Sampling Theory with Applications: How Michael Selected Amy if you want to see both together at one location. Otherwise please go through the 1179 references cited in the back of this monograph. It is obvious that similarly GREG and TRUMP are also design unbiased for such designs in case one wishes to make. Linear Regression Estimator is BLUE (Best Linear Unbiased Estimator) for any design.
@Dey: For some designs, the ratio estimator as well as linear regression estimators are also design unbiased. Follow Advanced Sampling Theory with Applications: How Michael Selected Amy if you want to see both together at one location. Otherwise go through the 1179 references cited in the back of this monograph. It is obvious that similarly GREG and TRUMP are also design unbiased for such designs. Linear Regression Estimator is BLUE (Best Linear Unbiased Estimator) for any design.
@Dr. Dey Replied: Ha Ha....look that is the advantage of the HT estimator....you have to implement a sampling design to make the ratio or the regression estimator unbiased, whereas for any without replacement sampling design, the HT estimator is unbiased.
@Dr. Dey: I do not see any advantage of such designs because then both the ratio and the regression loose efficiency.
Neither Simple Random Sampling with Replacement (SRSWR), nor Probability Proportional to Size with Replacement (PPSWR) are special cases of the HT estimator.
The question is still there: Why is the HT estimator so much popular?
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