Unordering of Estimators in Sampling Theory: Revisited

Article Type

Research Article

Publication Title

Journal of Statistical Theory and Practice


Rao–Blackwellization, a term credited to C. R. Rao based on his 1945 ‘breakthrough’ paper published in the Bulletin of the Calcutta Mathematical Society, besides providing improved estimators in conventional, adaptive, link-tracing, size-biased sampling theories, found applications in post simulation improvement of Monte Carlo methods, cross validation and non parametric boot strapping, particle filtering, stereology, data compression, Rao-Blackwellized Field Goal percentage estimator (RB-FG %), Rao-Blackwellized Gaussian Smoothing, Rao–Blackwellized Parts-Constellation Tracker, Rao-Blackwellized Tempered Sampling (RTS) and a host of others. In this paper, we shall consider applications related to improving of estimators in finite population sampling theory. Taking cue from Basu (1958) wherein he showed that the ‘order statistic ‘(sample units in ascending order of their labels) is a sufficient statistic, Pathak (Sankhya A 23:409–414, 1961) in the context of sampling from finite populations,first noticed that ‘any estimator which is not a function of the order statistic’, can be uniformly improved by the use of Rao–Blackwellization technique. See also Sinha and Sen (Sankhya [B] 51: 65–83, 1989) who go beyond variance comparisons and generalize to convex loss functions. In this paper, we shall revisit some of the estimators in Probability Proportional to Size sampling With Out Replacement (PPSWOR) schemes and show how Rao–Blackwellization provides improved estimators.



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