A unifying framework for k-statistics, polykays and their multivariate generalizations
Di Nardo, Elvira ; Guarino, Giuseppe ; Senato, Domenico
Bernoulli, Tome 14 (2008) no. 1, p. 440-468 / Harvested from Project Euclid
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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.
Publié le : 2008-05-15
Classification:  cumulants,  k-statistics,  polykays,  symmetric polynomials,  umbral calculus 
@article{1208872113,
     author = {Di Nardo, Elvira and Guarino, Giuseppe and Senato, Domenico},
     title = {A unifying framework for k-statistics, polykays and their multivariate generalizations},
     journal = {Bernoulli},
     volume = {14},
     number = {1},
     year = {2008},
     pages = { 440-468},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1208872113}
}

Di Nardo, Elvira; Guarino, Giuseppe; Senato, Domenico. A unifying framework for k-statistics, polykays and their multivariate generalizations. Bernoulli, Tome 14 (2008) no. 1, pp.  440-468. http://gdmltest.u-ga.fr/item/1208872113/