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.

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

DI NARDO, Elvira;
2008-01-01

Abstract

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.
2008
14
2
440
468
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.bj/1208872113
cumulants, k-statistics, polykays, symmetric polynomials, umbral calculus
E. DI NARDO; G. GUARINO G; D. SENATO
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1561347
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