Random matrices by MA models and compound free Poisson laws

• Autorzy: Hasegawa A. , Sakuma N. , Yoshida H.
• Języki publikacji: EN

Abstrakty

EN

Recently, Pfaffel and Schlemm have investigated the Marchenko-Pastur type limit (n → ∞ and lim_n→∞ n/p = λ > 0) of the sample covariance matrix p⁻¹X_n^t X_n, where X_n is the p × n random matrix with dependence such that each row of X_n is given by a certain linear process. They have also determined the limit spectral measure by giving the functional equation for its Stieltjes transform. In this paper, we will see that such a limit spectral measure is a compound free Poisson law and, in the case where dependence is given by MA modeled Gaussian process, the sample covariance matrix can be regarded as compound Wishart matrix and, hence, gives the random matrix model for a compound free Poisson law. We will also give an application of compound Wishart matrix to the statistical data analysis of times series.

Słowa kluczowe

EN

random matrix with dependent entries; asymptotic freeness; compound free Poisson laws; free Meixner laws

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2013
• Tom: Vol. 33, Fasc. 2
• Strony: 243--254
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Hasegawa A.

• Department of Information Sciences, Ochanomizu Universitym, 2-1-1, Otsuka, Bunkyo, Tokyo 112-8610 Japan

autor

Sakuma N.

• Department of Mathematics, Aichi University of Education, 1 Hirosawa, Igaya-cho, Kariya-shi 448-8542 Japan

autor

Yoshida H.

• Department of Information Sciences, Ochanomizu University, 2-1-1, Otsuka, Bunkyo, Tokyo 112-8610 Japan

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).