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

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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.
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)

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Combinatorics, Statistics Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/161188

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0607623
 http://arxiv.org/abs/math/0607623
 Bernoulli 2008, Vol. 14, No. 2, 440-468
 doi:10.3150/07-BEJ6163

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arXiv