Mathematics – Combinatorics
Scientific paper
2006-07-25
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.
Guarino Giuseppe
Nardo Elvira Di
Senato Domenico
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