An Essay on the Logical Foundations of Survey Sampling, Part One*

Basu, Debabrata

doi:10.1007/978-1-4419-5825-9_24

Cited by 56 publications

(83 citation statements)

References 12 publications

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“…This could be viewed as a modelassisted approach, which we discuss in more detail in Section 3. The widely cited Basu elephant example (Basu, 1971, Hájek, 1971) provides an extreme example in which the HT estimator performs poorly in a situation in which the responses y k are not related to the sampling probabilities π k . Briefly, a fictional circus owner would like to estimate the weight of his 50 strong herd of elephants, based on measuring a single elephant.…”

Section: Switching the Paradigmsmentioning

confidence: 99%

Introduction to the Design and Analysis of Complex Survey Data

Skinner¹,

Wakefield²

2017

Statist. Sci.

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Abstract. We give a brief overview of common sampling designs used in a survey setting, and introduce the principal inferential paradigms under which data from complex surveys may be analyzed. In particular, we distinguish between design-based, model-based and model-assisted approaches. Simple examples highlight the key differences between the approaches. We discuss the interplay between inferential approaches and targets of inference and the important issue of variance estimation.

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Section: Switching the Paradigmsmentioning

confidence: 99%

Introduction to the Design and Analysis of Complex Survey Data

Skinner¹,

Wakefield²

2017

Statist. Sci.

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“…Bayesians also spent a lot of time writing about toy problems, e.g., Basu's example of the weights of elephants (Basu 1971). From the other direction, classical statisticians felt that Bayesians were idealistic and detached from reality.…”

Section: The Pluralist's Dilemmamentioning

confidence: 99%

Statistical inference from a Dempster–Shafer perspective

Dempster¹

2014

Past, Present, and Future of Statistical Science

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The field of statistics continues to be divided into competing schools of thought. In theory one might imagine choosing the uniquely best method for each problem as it arises, but in practice we choose for ourselves (and recommend to others) default principles, models, and methods to be used in a wide variety of settings. This article briefly considers the informal criteria we use to decide what methods to use and what principles to apply in statistics problems. Statistics: The science of defaultsApplied statistics is sometimes concerned with one-of-a-kind problems, but statistical methods are typically intended to be used in routine practice. This is recognized in classical theory (where statistical properties are evaluated based on their long-run frequency distributions) and in Bayesian statistics (averaging over the prior distribution). In computer science, machine learning algorithms are compared using cross-validation on benchmark corpuses, which is another sort of reference distribution. With good data, a classical procedure should be robust and have good statistical properties under a wide range of frequency distributions, Bayesian inferences should be reasonable even if averaging over alternative choices of prior distribution, and the relative performance of machine learning algorithms should not depend strongly on the choice of corpus.How do we, as statisticians, decide what default methods to use? Here I am using the term "method" broadly, to include general approaches to statistics (e.g., Bayesian, likelihood-based, or nonparametric) as well as more specific choices of models (e.g., linear regression, splines, or Gaussian processes) and options within a model or method (e.g., model averaging, L 1 regularization, or hierarchical partial pooling). There are so many choices that it is hard to imagine any statistician carefully weighing the costs and benefits of each before 291

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“…Indeed, in the last decades there has been some confusion concerning the general applicability of the HT estimator. This confusion was provoked by Basu (1971) in his famous elephant fable: A circus owner plans to ship 50 adult elephants and therefore needs a rough estimate of their total weight. As weighing elephants is not so easy, the owner intuitively plans to weigh only one elephant and to multiply the result with 50.…”

Section: Once More Basu's Elephantsmentioning

confidence: 99%

“…Though the confusions about Basu's fable have been solved at the latest with Rao's (1999) article and its subsequent discussion, it is still interesting to take a look at the rejoinder of Basu's (1971) essay, in which he vehemently denied that the 'unrealistic sampling plan' was responsible for the failure of the HorvitzThompson estimator. Basu defended, in contrary, the circus statistician's sampling plan, as it ensures a representative sample, which would not have been guaranteed using Koop's average of ratios estimator.…”

Section: A General Dilemma?mentioning

confidence: 99%

On design-weighted local fitting and its relation to the Horvitz-Thompson estimator

Einbeck¹,

Augustin²

2009

STAT SINICA

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Weighting is a widely used concept in many fields of statistics and has frequently caused controversies on its justification and benefit. In this paper, we analyze design-weighted versions of the well-known local polynomial regression estimators, derive their asymptotic bias and variance, and observe that the asymptotically optimal weights are in conflict with (practically motivated) weighting schemes previously proposed in the literature. We investigate this conflict using theory and simulation, and find that the problem has a surprising counterpart in sampling theory, leading us back to the discussion on the Horvitz-Thompson estimator and Basu's (1971) elephants. In this light one might consider our results as an asymptotic and nonparametric version of the Horvitz-Thompson theorem. The crucial point is that bias-minimizing weights can make estimators extremely vulnerable to outliers in the design space and have therefore to be used with particular care.

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An Essay on the Logical Foundations of Survey Sampling, Part One*

Cited by 56 publications

References 12 publications

Introduction to the Design and Analysis of Complex Survey Data

Introduction to the Design and Analysis of Complex Survey Data

Statistical inference from a Dempster–Shafer perspective

On design-weighted local fitting and its relation to the Horvitz-Thompson estimator

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