Abstract
“A circus owner is planning to ship his 50 adult elephants and so he needs a rough estimate of the total weight of the elephants ”…, so begins Example 3 in Basu (1971), the most colorful and striking illustration of Basu’s challenges to the design-based analysis of sample survey data. The full story is included in the box for easy reference. The owner decides to take a sample of size n=1 (“As weighing an elephant is a cumbersome process”) and is talked out of a non-random sample (select Sambo, the elephant that had the average weight 3 years before) and the model-based estimate (50 y) into an unequal probability sample (select Sambo with probability 99/100 and any of the other elephants with probability 1/4900) and the Horvitz-Thompson estimator (100 y /99 if Sambo is selected and 4900y if any other elephant is selected). The point of the story is summarised in Figure 1 which shows the log-sampling distributions (i.e. the sampling distributions of the log of the estimators) for samples of size 1 of the model-based estimator and the Horvitz-Thompson estimator for a troupe of 50 elephants. (We plot the log-sampling distributions to improve the visual impact.) On this scale, the model-based estimator is very close to the actual total weight (indicated by an arrow) but, and this is Basu’s elegantly made point, the design-unbiased Horvitz-Thompson is far from the actual total weight in every possible sample. The design-based optimality of the Horvitz-Thompson estimator is no consolation to either the circus owner or the “unhappy statistician” who, Basu tells us, “lost his circus job (and perhaps became a teacher of statistics!)”.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Basu, D. (1958). Sampling with and without replacements. Sankhya 20, 287–294.
Basu, D. (1969). Role of the sufficiency and likelihood principles in sample survey theory. Sankhya 31, 441–454.
Basu, D. (1971). An essay on the logical foundations of survey sampling, part I (with discussion). In Foundations of Statistical Inference, eds V.P. Godambe and D.A. Sprott, Toronto: Holt, Rinehart and Winston, 203–243.
Basu, D. (1978). On the relevance of randomization in data analysis (with discussion). In Survey Sampling and Measurement, ed N.K. Namboodiri, New York: Academic Press, 267–339.
Basu, D. and Ghosh, J.K. (1967). Sufficient statistics in sampling from a finite universe. Bull. Int. Statist. Inst. 42, 850–859.
Royall, R.M. (1976). Current advances in sampling theory: Implications for human observational studies (with discussion). Amer. J. Epidem. 104 463–477.
Rubin, D.B. (1978). Bayesian inference for causal effects: The role of randomisation. Ann. Statist., 6 34–58.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Welsh, A. (2011). Basu on Survey Sampling. In: DasGupta, A. (eds) Selected Works of Debabrata Basu. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5825-9_11
Download citation
DOI: https://doi.org/10.1007/978-1-4419-5825-9_11
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-5824-2
Online ISBN: 978-1-4419-5825-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)