Expectation and Estimation of Product Moments in Sampling from a Finite Population

Abstract

This article presents improvements in and an extension of results published in this journal by Nath in 1968 and 1969 and by Raghunandanan and Srinivasan in 1973 for two general multivariate expectation problems and a related estimation problem. Our presentation applies a modification of basic theory developed by H.C. Carver and his students at the University of Michigan in the 1930's and gives more compact and adequate solutions to the expectation problems. Using related and recently developed theory on unbiased estimation, results are obtained more directly for the estimation problem. Estimates of the lower-order moments thus obtained can be used to provide answers to two general expectation problems and an estimation problem.

Key Words:

• Sampling from a finite population
• Expected value
• Unbiased estimate
• Partition notation for power sums
• Carver functions and modification