The objective of this article is a critical appraisal of the classical Horvitz-Thompson (HT) estimator used in survey sampling, and examine when and where it is effective. For illustration, we have brought in the hilarious circus example of Basu's[1] where the HT estimator led to a disastrous result. We have pointed out what went wrong with this example and, in the process, have also discussed what one needs for a successful application of the HT estimator. We also provide a model-based interpretation of the HT estimator, and again discuss the success or failure of the HT estimator from a model-based perspective.
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LittleRJA. To Model or Not to Model? Competing Modes of Inference for Finite Population Sampling. J Amer Stat Assoc.2004; 99(2): 546–556.
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GhoshMSinhaBK. On the Consistency between Model- and Design-based Estimators in Survey Sampling. Comm Stat, Theo Meth.1989; 19(2): 689–702.
