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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 441, Pages 163–186
(Mi znsl6232)
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This article is cited in 1 scientific paper (total in 1 paper)
Circular unitary ensembles: parametric models and their asymptotic maximum likelihood estimates
R. Dakovica, M. Denkerb, M. Gordinc a Georg-August-Universität Göttingen
b The Pennsylvania State University
c Steklov Institute of Mathematics, St. Petersburg
Abstract:
Parametrized families of distributions for the circular unitary ensemble in random matrix theory are considered which are connected to Toeplitz determinants and which have many applications in mathematics (for example to the longest increasing subsequences of random permutations) and physics (for example to nuclear physics and quantum gravity). We develop a theory for the unknown parameter estimated by an asymptotic maximum likelihood estimator, which, in the limit, behaves as the maximum likelihood estimator if the latter is well defined and the family is sufficiently smooth. They are asymptotically unbiased and normally distributed, where the norming constants are unconventional because of long range dependence.
Key words and phrases:
circular unitary ensemble, Toeplitz determinant, maximum likelihood estimator, normal distribution, long range dependence.
Received: 30.09.2015
Citation:
R. Dakovic, M. Denker, M. Gordin, “Circular unitary ensembles: parametric models and their asymptotic maximum likelihood estimates”, Probability and statistics. Part 22, Zap. Nauchn. Sem. POMI, 441, POMI, St. Petersburg, 2015, 163–186; J. Math. Sci. (N. Y.), 219:5 (2016), 714–730
Linking options:
https://www.mathnet.ru/eng/znsl6232 https://www.mathnet.ru/eng/znsl/v441/p163
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