General expectation of partitional moment functions

Abstract

The paper provides a general theory for expected values of linear functions of products of sample power sums in terms of products of population power sums -all given symbolically by partitions. This approach is so general that the results can be applied to any sample moment function under any sampling law from a finite or infinite, univariate or multivariate, population. With simple modification, an unbiased estimate of the population moment function in the above situations can also be determined. The results provided are general enough to cover most of the work done so far on moments of moments. The results feature coefficients of individual terms, thereby avoiding accumulated algebraic errors, frequent in earlier works.