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A Better Estimator of Population Mean with Power Transformation Based on Ranked Set Sampling

100%
Mehta (Ranka) N., Mandowara V. L.
Statistics in Transition new series
|
2012
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vol. 13
|
issue 3
551-558
EN
Ranked set sampling (RSS) was first suggested by McIntyre (1952) to increase the efficiency of estimate of the population mean. It has been shown that this method is highly beneficial to the estimation based on simple random sampling (SRS). There has been considerable development and many modifications were done on this method. This paper presents a modified ratio estimator using prior value of coefficient of kurtosis of an auxiliary variable x, with the intention to improve the efficiency of ratio estimator in ranked set sampling. The first order approximation to the bias and mean square error (MSE) of the proposed estimator are obtained. A generalized version of the suggested estimator by applying the Power transformation is also presented.
2
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Estimating the population mean using a continuous sampling design dependent on an auxiliary variable

75%
Wywiał J. L.
Statistics in Transition new series
|
2020
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vol. 21
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issue 5
1-16
EN
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.
3
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Estimation of Mean on The Basis of Conditional Simple Random Sample

63%
Wywiał J. L.
Statistics in Transition new series
|
2016
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vol. 17
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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.
4
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Sampling Designs Proportionate to Sum of Two Order Statistics of Auxiliary Variable

63%
Wywiał J. L.
Statistics in Transition new series
|
2013
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vol. 14
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issue 2
231-248
EN
In this paper the case of a conditional sampling design proportional to the sum of two order statistics is considered. Several strategies including the Horvitz-Thompson estimator and ratio-type estimators are discussed. The accuracy of these estimators is analyzed on the basis of computer simulation experiments.
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