6 Summary
Ken Brewer
In conclusion, we can see that survey sampling, over its relatively short history, has been remarkably vulnerable to controversies. In the first instance there was opposition to the notion that there should be any sampling at all. The only valid source of statistical information was taken to be the complete collection. It took the determination of Kiaer, a person already in a senior position of authority, to break down the opposition to what was eventually demonstrated to be a valuable tool.
The second controversy was also due to the determination of just a few people. Neyman took the lead, but this time there were others who were involved. Bowley was certainly involved to start with, but Neyman seems to have had the more convincing arguments at the crucial time. They were controversial, even to begin with, and I am certainly not impressed with them now, but at the time he found a ready disciple in Hansen, who dominated the sampling fraternity for decades, at least until the mid-1970s.
The third controversy is still in progress and it is not altogether clear as to how it will turn out, but my current preference (at least for middling-sized samples) would be to use the prediction and randomization estimators combined.
In summary, both the HT and the BLUP can be useful in different situations. The BLUP makes sense to use when the sample size is small, and a model is desperately needed. The HT provides protection against prediction-model failure as the sample grows large. A prudent statistician would combine the principles of both.
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