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  1. 2 Statistics in Transition new series

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  1. 2 Wywiał J. L.

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  1. 1 2016

  2. 1 2012

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Application of Order Statistics of Auxiliary Variable to Estimation the Population Mean

100%
Wywiał J. L.
Statistics in Transition new series
|
2012
|
vol. 13
|
issue 2
279-286
EN
Estimation of the population average in a finite population by means of sampling strategies dependent on an auxiliary variable highly correlated with a variable under study is considered. The sample is drawn with replacement on the basis of the probability distribution of an order statistic of the auxiliary variable. Observations of the variable under study are the values of the concomitant of the order statistic. The mean of the concomitant values is the estimator of a population mean of the variable under study. The expected value and the variance of the estimator are derived. The limit distributions of the considered estimators were considered. Finally, on the basis of simulation analysis, the accuracy of the estimator is considered.
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Estimation of Mean on The Basis of Conditional Simple Random Sample

84%
Wywiał J. L.
Statistics in Transition new series
|
2016
|
vol. 17
|
issue 3
411-428
EN
Estimation of the population mean in a finite and fixed population on the basis of the conditional simple random sampling design dependent on order statistics (quantiles) of an auxiliary variable is considered. Properties of the well-known Horvitz-Thompson and ratio type estimators as well as the sample mean are taken into account under the conditional simple random sampling designs. The considered examples of empirical analysis lead to the conclusion that under some additional conditions the proposed estimation strategies based on the conditional simple random sample are usually more accurate than the mean from the simple random sample drawn without replacement.
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