The Annals of Statistics

Natural statistics for spectral samples

E. Di Nardo, P. McCullagh, and D. Senato

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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.

Article information

Ann. Statist., Volume 41, Number 2 (2013), 982-1004.

First available in Project Euclid: 29 May 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 46L53: Noncommutative probability and statistics
Secondary: 62F12: Asymptotic properties of estimators

Random matrix cumulant of traces free cumulant polykays


Di Nardo, E.; McCullagh, P.; Senato, D. Natural statistics for spectral samples. Ann. Statist. 41 (2013), no. 2, 982--1004. doi:10.1214/13-AOS1107.

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