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Sampling with probabilities proportional to the variable of interest
Moors,J.J.A. Smeets,R. Boekema,F.W.M.
Moors,J.J.A.
Smeets,R.
Boekema,F.W.M.
Abstract
To estimate the mean sojourn time, a sample of Tilburg fair visitors was asked for the duration of their stay on the fair grounds. The longer a visitor's sojourn, the larger his/her probability of being interviewed will be; therefore, longer sojourn times will be overrepresented in the sample. As a consequence, the arithmetic sample mean is not a suitable estimator. The paper places this problem against a theoretical background. As a better estimator the harmonic mean of the observed sojourn times is presented. In addition, a variance estimator is given. The properties of these estimators are difficult to derive analytically. Instead, their behaviour is studied in a number of examples.
Description
Pagination: 15
Date
1996
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Volume Title
Publisher
Unknown Publisher
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717.pdf
Adobe PDF, 218.36 KB
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Keywords
Probability, Estimation, Sampling, statistics
Citation
Moors, J J A, Smeets, R & Boekema, F W M 1996, Sampling with probabilities proportional to the variable of interest. Research memorandum / Tilburg University, Faculty of Economics and Business Administration, vol. FEW 717, vol. FEW 717, Unknown Publisher.