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Estimators and Relative Efficiencies in Models of Overlapping Samples

  • U. Kamps
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

In a model describing the situation of overlapping samples four unbiased estimators of the expectation of underlying random variables are examined based on different amount of information about the problem. Mallows, Vardi (1982) state an inequality for the variances of three estimators leading to a bound for relative efficiencies. In order to compare the estimators and to appraise the disadvantage that arises, if an auxiliary estimator is used instead of the optimal one, a similar inequality is given with respect to another triplet of estimators, and equality of any two estimators is characterized by means of column sums of certain matrices. Several examples are shown, and in special models of overlapping samples the results are applied, and relative efficiences are plotted as functions of problem parameters.

Keywords

Relative Efficiency Unbiased Estimator Chebyshev Polynomial Incidence Matrix Problem Parameter 
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Bibliography

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1991

Authors and Affiliations

  • U. Kamps
    • 1
  1. 1.Institut für Statistik und WirtschaftsmathematikAachen University of TechnologyAachenGermany

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