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Mean Value Estimation Using Two-Phase Samples with Missing Data in Both Phases

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Abstract

The phenomenon of nonresponse in a sample survey reduces the precision of parameter estimates and causes the bias. Several methods have been developed to compensate for these effects. An important technique is the double sampling scheme introduced by Hansen and Hurwitz (J. Am. Stat. Assoc. 41, 517–529, 1946) which relies on subsampling of nonrespondents and repeating efforts to collect data from subsampled units. Several generalizations of this procedure have been proposed, including the application of arbitrary sampling designs considered by Särndal et al. (Model Assisted Survey Sampling, 1992). Under the assumption of complete response in the second phase, the population mean estimator constructed using data from both phases is unbiased.

In this paper the properties of the mean value estimator under two-phase sampling are investigated for the case of the above assumption not being met. Expressions for bias and variance are obtained for general two-phase sampling procedure involving arbitrary sampling designs in both phases. Stochastic nonresponse governed by separate response distributions in both phases is assumed. Some special cases are discussed.

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References

  1. Cassel, C.M., Särndal, C.E., Wretman, J.: Some uses of statistical models in connection with the nonresponse problem. In: Incomplete Data in Sample Surveys. Academic, New York (1983)

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Authors and Affiliations

  1. Department of Statistics, University of Economics, Katowice, Poland

    Wojciech Gamrot

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  1. Wojciech Gamrot
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Correspondence to Wojciech Gamrot.

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Gamrot, W. Mean Value Estimation Using Two-Phase Samples with Missing Data in Both Phases. Acta Appl Math 96, 215–220 (2007). https://doi.org/10.1007/s10440-007-9110-5

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  • DOI: https://doi.org/10.1007/s10440-007-9110-5

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