A General Completeness Theorem in Sampling Theory
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1983 · Volume 45 · Issue 3
DOI: 10.1111/j.2517-6161.1983.tb01263.x
Abstract
Generalized symmetry of designs and estimators is defined to be invariance under a subgroup of the group of label permutations. A simple sufficient condition in terms of the design is given for the generalized order statistic, of which each generalized symmetric estimator is a function, to be complete. This condition is shown also to be necessary when the range of possible values for each characteristic is sufficiently large.
Keywords
completeness, finite populations, permutation subgroup, separably transformable sampling design, order statistic, symmetric estimator
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