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Estimation of Domain Means on The Basis of Strategy Dependent on Depth Function of Auxiliary Variables’ Distribution

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Wywiał J. L.

Statistics in Transition new series

2011

vol. 12

issue 1

127-138

The paper deals with the problem of estimation of a domain means in a finite and fixed population. We assume that observations of a multidimensional auxiliary variable are known in the population. The proposed estimation strategy consists of the well known Horvitz-Thompson estimator and the non-simple sampling design dependent on a synthetic auxiliary variable whose observations are equal to the values of a depth function of the auxiliary variable distribution. The well known spherical and Mahalanobis depth functions are considered. A sampling design is proportionate to the maximal order statistic determined on the basis of the synthetic auxiliary variable observations in a simple sample drawn without replacement. A computer simulation analysis leads to the conclusion that the proposed estimation strategy is more accurate for domain means than the well known simple sample means.

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1 Statistics in Transition new series

1 2011

1 Wywiał J. L.

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Estimation of Domain Means on The Basis of Strategy Dependent on Depth Function of Auxiliary Variables’ Distribution