Estimators and Relative Efficiencies in Models of Overlapping Samples
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.
KeywordsRelative Efficiency Unbiased Estimator Chebyshev Polynomial Incidence Matrix Problem Parameter
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- Pólya, G., Szegö, G. (1964): Aufgaben und Lehrsätze aus der Analysis, Erster Band. Springer, Berlin.Google Scholar