Symulacyjna analiza dokładności oceny wartości przeciętnej za pomocą strategii zależnych od różnicy statystyk pozycyjnych zmiennej dodatkowej
Accuracy of population mean estimation on the basis of strategies dependent on difference of auxiliary variable order statistics. Simulation analysis

Summary/Abstract: Estimation of the population average in a finite population by means of sampling strategy dependent on the sample quantile of an auxiliary variable is considered. The sampling design is proportionate to the difference of two quantiles of an auxiliary variable. The derived inclusion probabilities are applied to estimation the population mean using the well known Horvitz-Thompson estimator which is called Horvitz-Thompson-regression estimator. The next estimator was the regression estimator whose parameters are assessed by the Horvitz-Thompson estimator. Particularly, the quantile-regression estimator is defined as the function of the slope coefficient dependent on the quantiles (order statistics) of the auxiliary variable. The construction of the slope coefficient was inspired by the estimator of this coefficient considered by Hellwig. The simulation analysis of accuracy estimators leads to conclusion that in general Horvitz-Thompson-regression and the ordinary regression one are the best among the considered ones.

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