A Model for Studying Robustness of Estimators and Informativeness of Labels in Sampling with Varying Probabilities

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1972 · Volume 34 · Issue 2

DOI: 10.1111/j.2517-6161.1972.tb00907.x

Abstract

This paper presents a model for investigating how information contained in the labels of a finite population may be utilized in order to reduce variance when sampling from a finite population with varying probabilities. The model assumes a population ofNvalues of a characteristicXgiven asXi=Yi+ Zi(i= 1, …,N), where the mean ofXis to be estimated. HereYiis a systematic component in the sense that its relation to the labeliisa prioriknown, or intelligently guessed at, whileZiis an error component. In the with-replacement case, a sample of labels is selected with possibly unequal probabilitiespi,(i= 1, …,N)attached to the various labels in each of thendraws. Assuming thatNis reasonably large, the variance of the usual estimator is studied under various assumptions about the shape of the continuous distribution approximating theY-distribution (e.g. gamma, Pareto, Weibull shapes), various assumptions about the influence of the error componentZ, and different designs for distributing the probabilitiesPiamong theNlabels.

Keywords

finite population, varying probabilities, regression model information in labels, robustness of estimators, design function, gamma, pareto, weibull

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