Spectral sampling is associated with the group of unitary transformations acting on matrices in the same way that simple random sampling is associated with the symmetric group acting on vectors. This parallel extends to symmetric functions of spectral samples, k-statistics and polykays. According to the moment method em- ployed within random matrix theory, we introduce cumulants of a random matrix as cumulants of its trace powers and construct spectral polykays as unbiased estimators of their product. When referred to spectral samples, we prove that spectral polykays are natural statistics and return products of free cumulants when the sampling is from an innite population. Moreover we dene generalized cumulants of spectral polykays and study their asymptotic behaviour.

Natural statistics for spectral samples

DI NARDO, Elvira;SENATO PULLANO, Domenico
2013-01-01

Abstract

Spectral sampling is associated with the group of unitary transformations acting on matrices in the same way that simple random sampling is associated with the symmetric group acting on vectors. This parallel extends to symmetric functions of spectral samples, k-statistics and polykays. According to the moment method em- ployed within random matrix theory, we introduce cumulants of a random matrix as cumulants of its trace powers and construct spectral polykays as unbiased estimators of their product. When referred to spectral samples, we prove that spectral polykays are natural statistics and return products of free cumulants when the sampling is from an innite population. Moreover we dene generalized cumulants of spectral polykays and study their asymptotic behaviour.
2013
File in questo prodotto:
File Dimensione Formato  
natural.pdf

accesso aperto

Tipologia: Documento in Post-print
Licenza: DRM non definito
Dimensione 267.54 kB
Formato Adobe PDF
267.54 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11563/44435
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 5
social impact