Estimating the population mean using a continuous sampling design dependent on an auxiliary variable

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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics, Statistics & Probability

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VOLUME 21 , ISSUE 5 (December 2020) > List of articles

Estimating the population mean using a continuous sampling design dependent on an auxiliary variable

Janusz L. Wywiał

Keywords : continuous sampling design, Horvits-Thompson estimator, inclusion density, sampling scheme, bivariate gamma distribution, ratio estimator

Citation Information : Statistics in Transition New Series. Volume 21, Issue 5, Pages 1-16, DOI: https://doi.org/10.21307/stattrans-2020-052

License : (CC BY-NC-ND 4.0)

Received Date : 17-March-2020 / Accepted: 07-August-2020 / Published Online: 20-December-2020

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ABSTRACT

Continuous distribution of variables under study and auxiliary variables are considered. The purpose of the paper is to estimate the mean of the variable under study using a sampling design which is dependent on the observation of a continuous auxiliary variable in the whole population. Auxiliary variable values observed in this population allow to estimate the inclusion density function of the sampling design. The variance of the continuous version of the Horvitz-Thompson estimator under the proposed sampling design is compared with the variance of the mean of a simple random sample. The accuracy of the estimation strategies is analysed by means of simulation experiments.

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