Robust inference under r-size-biased sampling without replacement from finite population

P. Economou, G. Tzavelas and A. Batsidis

Journal of Applied Statistics, 2020, vol. 47, issue 13-15, 2808-2824

Abstract: The case of size-biased sampling of known order from a finite population without replacement is considered. The behavior of such a sampling scheme is studied with respect to the sampling fraction. Based on a simulation study, it is concluded that such a sample cannot be treated either as a random sample from the parent distribution or as a random sample from the corresponding r-size weighted distribution and as the sampling fraction increases, the biasness in the sample decreases resulting in a transition from an r-size-biased sample to a random sample. A modified version of a likelihood-free method is adopted for making statistical inference for the unknown population parameters, as well as for the size of the population when it is unknown. A simulation study, which takes under consideration the sampling fraction, demonstrates that the proposed method presents better and more robust behavior compared to the approaches, which treat the r-size-biased sample either as a random sample from the parent distribution or as a random sample from the corresponding r-size weighted distribution. Finally, a numerical example which motivates this study illustrates our results.

Date: 2020
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DOI: 10.1080/02664763.2019.1711031

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