Abstract
In this dissertation two special purpose biased estimators for estimating population means from small random samples are formulated and analytically compared to the arithmetic mean. The first estimator formulated is a weighted average of the sample mean and the square of the average square roots of the sampled observations. The values of the weighting constants were optimized for various positive populations for sample sizes of n = 2 to n = 20 to determine weighting values which are applicable to a broad class of positive populations. The second estimator formulated is a weighted average of the sample mean and the cube of the average cube roots of the sampled observations. In this case too, the weighting constants were optimized for various populations and sample sizes. Graphs and tables are presented showing the optimum values of the weighting constants for the various populations and sample sizes.
Jenkins, Omer Carson (1972). A new class of minimum mean square error estimators. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -184691.