Symbolic computation of moments of sampling distributions

TL;DR

This paper introduces a symbolic computation method using umbrae indexed by multisets to efficiently calculate moments of sampling distributions, significantly reducing computational effort compared to existing methods.

Contribution

It develops a novel symbolic approach linking multisets and integer partitions to optimize the calculation of moments in sampling distributions.

Findings

Faster computation of moments compared to traditional methods

Reduction in unnecessary calculations during symbolic evaluation

Effective use of umbrae and multisets for statistical estimators

Abstract

By means of the notion of umbrae indexed by multisets, a general method to express estimators and their products in terms of power sums is derived. A connection between the notion of multiset and integer partition leads immediately to a way to speed up the procedures. Comparisons of computational times with known procedures show how this approach turns out to be more efficient in eliminating much unnecessary computation.