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Linear combination of estimators in probability proportional to sizes sampling to estimate the population mean and its robustness to optimum value


  • Satish Kumar Agarwal


  • Mariam Al Mannai


In this paper we have studied the gain of efficiency and the relative bias of linear weighted estimators over conventional estimators under probability proportional to size with replacement (ppswr) sampling for a wide variety of populations. The five number summary statistics for the relative bias and the relative efficiency over conventional estimators is given for different magnitude of correlation coefficients. The computational study shows that there is a considerable gain in the efficiency of linear weighted estimators over conventional estimators. To develop the confidence of survey practitioners on linear weighted estimator, the computational study is extended to see the robustness of the linear weighted estimator by deviating the optimum value of the weight up to 50% on either side.

Suggested Citation

  • Satish Kumar Agarwal & Mariam Al Mannai, 2009. "Linear combination of estimators in probability proportional to sizes sampling to estimate the population mean and its robustness to optimum value," Statistica, Department of Statistics, University of Bologna, vol. 69(1), pages 59-71.
  • Handle: RePEc:bot:rivsta:v:69:y:2009:i:1:p:59-71

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