The symmetrized Des Raj estimator for a finite population total based on a PPSWOR sample of size two is shown to be admissible within (i) the class of all linear estimators and (ii) the class of all unbiased estimators. In this connection we have obtained a class of admissible linear estimators of the population total which includes the sample mean multiplied by the population size and the classical ratio estimator for any arbitrary sampling design.

A sufficient condition for admissibilitY is given for unbiased estimators of finite population parameters when sample size is at most two. The result is used to check admissibility of several unbiased estimators of population totals.

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On the Admissibility of the Symmetrized Des Raj Estimator for PPSWOR Samples of Size Two

Admissibility of Unbiased Estimators in Finite Population Sampling for Samples of Size at Most two

3 Optimality of sampling strategies

SOME SAMPLING DESIGNS AND ESTIMATION PROBLEMS Hassan D. Lakkis Old Dominion University, 1994 Director: Dr. Ram C. Dahiya In the first chapter we review some standard estimators in sampling from a fin ite population, and some design-based estimators in sampling from a continuous universe. In concert w ith the theory initiated by professor Douglas Robson (personal communication) and later presented by Cordy (1993), we consider design-based variance estimation for probability sampling from a continuous and spatially dis­ tributed universe. Using this theory in chapter two, the sampling design of one random point from each cell of a translated grid is investigated and the problem of edge effects on estimation is illustrated with examples. Also in chapter four, stan­ dard systematic sampling methods from a finite population are reviewed. Then, for systematic samples drawn from a continuous universe, a new approach for in ­ vestigating the estimators of the parameters of interest is introduced. This new approach can be useful for deriving unbiased variance estimators for many spa­ tia l systematic sampling methods and allows for proposing new efficient systematic sampling designs. For these systematic sampling designs, we present the estimator of the population total and the estimator of the variance for a population w ith one dimension, and we derive in general these estimators for n-dimensional population. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Furthermore in chapter five, a mean-balanced sample of size two from each cell of a translated grid is investigated. Then an unbiased estimator of the population total is presented. Also, explicit formulas for the inclusion density functions axe derived. The problem of sampling from an ordered population of size N is considered in the th ird chapter. Let the response variable of interest be denoted by yu t/2, —, and the auxiliary variable be denoted by x i,X 2, ...,x^. Assuming that the values of the x variable are known for all units in the population, a sampling design is developed which accounts for the ordering of the units. Here, the probability for the i th unit to be selected in the sample depends on X{. Based on this design two unbiased estimators of the population total, T = Ya=i Vu 3X6 presented and exact expressions of the variances of these estimators are derived. Also non-negative unbiased estimators of the variances are provided. This is a new sampling design that does not exist in the literature. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

On the Admissibility of the Symmetrized Des Raj Estimator for PPSWOR Samples of Size Two

Citations

Admissibility of Unbiased Estimators in Finite Population Sampling for Samples of Size at Most two

3 Optimality of sampling strategies

Some Sampling Designs and Estimation Problems

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