A unifying framework for $k$-statistics, polykays and their multivariate generalizations
Combinatorics
2008-05-19 v3 Statistics Theory
Statistics Theory
Abstract
Through the classical umbral calculus, we provide a unifying syntax for single and multivariate -statistics, polykays and multivariate polykays. From a combinatorial point of view, we revisit the theory as exposed by Stuart and Ord, taking into account the Doubilet approach to symmetric functions. Moreover, by using exponential polynomials rather than set partitions, we provide a new formula for -statistics that results in a very fast algorithm to generate such estimators.
Keywords
Cite
@article{arxiv.math/0607623,
title = {A unifying framework for $k$-statistics, polykays and their multivariate generalizations},
author = {Elvira Di Nardo and Giuseppe Guarino and Domenico Senato},
journal= {arXiv preprint arXiv:math/0607623},
year = {2008}
}
Comments
Published in at http://dx.doi.org/10.3150/07-BEJ6163 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)