A new method for fast computing unbiased estimators of cumulants
Abstract
We propose new algorithms for generating -statistics, multivariate -statistics, polykays and multivariate polykays. The resulting computational times are very fast compared with procedures existing in the literature. Such speeding up is obtained by means of a symbolic method arising from the classical umbral calculus. The classical umbral calculus is a light syntax that involves only elementary rules to managing sequences of numbers or polynomials. The cornerstone of the procedures here introduced is the connection between cumulants of a random variable and a suitable compound Poisson random variable. Such a connection holds also for multivariate random variables.
Cite
@article{arxiv.0807.5008,
title = {A new method for fast computing unbiased estimators of cumulants},
author = {E. Di Nardo and G. Guarino and D. Senato},
journal= {arXiv preprint arXiv:0807.5008},
year = {2008}
}
Comments
A table with computational times, obtained with the forthcoming MathStatica release 2 (Colin Rose, private communication), has been added. In press Stat. Comp