A unifying framework for $k$-statistics, polykays and their multivariate generalizations

Details A unifying framework for $k$-statistics, polykays and their multivariate generalizations A unifying framework for $k$-statistics, polykays and their multivariate generalizations

2006-07-25

arxiv.org/abs/math/0607623v3

Bernoulli 2008, Vol. 14, No. 2, 440-468

Mathematics

Combinatorics

Published in at http://dx.doi.org/10.3150/07-BEJ6163 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ6163

Through the classical umbral calculus, we provide a unifying syntax for single and multivariate $k$-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 $k$-statistics that results in a very fast algorithm to generate such estimators.

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