The Annals of Statistics

Natural statistics for spectral samples

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

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Abstract

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

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

Dates
First available in Project Euclid: 29 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.aos/1369836967

Digital Object Identifier
doi:10.1214/13-AOS1107

Mathematical Reviews number (MathSciNet)
MR3099128

Zentralblatt MATH identifier
1287.60009

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

Keywords
Random matrix cumulant of traces free cumulant polykays

Citation

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. https://projecteuclid.org/euclid.aos/1369836967


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