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April 2013 Natural statistics for spectral samples
E. Di Nardo, P. McCullagh, D. Senato
Ann. Statist. 41(2): 982-1004 (April 2013). DOI: 10.1214/13-AOS1107


Spectral sampling is associated with the group of unitary transformations acting on matrices in much the same way that simple random sampling is associated with the symmetric group acting on vectors. This parallel extends to symmetric functions, $k$-statistics and polykays. We construct spectral $k$-statistics as unbiased estimators of cumulants of trace powers of a suitable random matrix. Moreover we define normalized spectral polykays in such a way that when the sampling is from an infinite population they return products of free cumulants.


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E. Di Nardo. P. McCullagh. D. Senato. "Natural statistics for spectral samples." Ann. Statist. 41 (2) 982 - 1004, April 2013.


Published: April 2013
First available in Project Euclid: 29 May 2013

zbMATH: 1287.60009
MathSciNet: MR3099128
Digital Object Identifier: 10.1214/13-AOS1107

Primary: 46L53 , 60B20
Secondary: 62F12

Keywords: cumulant of traces , free cumulant , polykays , Random matrix

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.41 • No. 2 • April 2013
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