A new method for fast computing unbiased estimators of cumulants

We propose new algorithms for generating k -statistics, multivariate k -statistics, polykays and multivariate polykays. The resulting computational times are very fast compared with procedures existing in the literature. Such speeding up is obtained by means of a symbolic method arising from the cla...

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Veröffentlicht in:Statistics and computing 2009-06, Vol.19 (2), p.155-165
Hauptverfasser: Di Nardo, E., Guarino, G., Senato, D.
Format: Artikel
Sprache:eng
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Zusammenfassung:We propose new algorithms for generating k -statistics, multivariate k -statistics, polykays and multivariate polykays. The resulting computational times are very fast compared with procedures existing in the literature. Such speeding up is obtained by means of a symbolic method arising from the classical umbral calculus. The classical umbral calculus is a light syntax that involves only elementary rules to managing sequences of numbers or polynomials. The cornerstone of the procedures here introduced is the connection between cumulants of a random variable and a suitable compound Poisson random variable. Such a connection holds also for multivariate random variables.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-008-9080-0