Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2013, Article ID 595912, 7 pages
http://dx.doi.org/10.1155/2013/595912
Research Article

Second-Order Moment Convergence Rates for Spectral Statistics of Random Matrices

College of Mathematics and Information, Henan University, Kaifeng 475000, China

Received 13 June 2013; Accepted 21 October 2013

Academic Editor: Henrik Kalisch

Copyright © 2013 Junshan Xie. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. Z. D. Bai, X. Y. Wang, and W. Zhou, “CLT for linear spectral statistics of Wigner matrices,” Electronic Journal of Probability, vol. 14, article 83, pp. 2391–2417, 2009. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. A. Guionnet and O. Zeitouni, “Concentration of the spectral measure for large matrices,” Electronic Communications in Probability, vol. 5, pp. 119–136, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. C. C. Heyde, “A supplement to the strong law of large numbers,” Journal of Applied Probability, vol. 12, pp. 173–175, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. A. Gut and A. Spătaru, “Precise asymptotics in the Baum-Katz and Davis laws of large numbers,” Journal of Mathematical Analysis and Applications, vol. 248, no. 1, pp. 233–246, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. A. Gut and A. Spătaru, “Precise asymptotics in the law of the iterated logarithm,” The Annals of Probability, vol. 28, no. 4, pp. 1870–1883, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. A. Gut and J. Steinebach, “Precise asymptotics–-a general approach,” Acta Mathematica Hungarica, vol. 138, no. 4, pp. 365–385, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  7. Y. S. Chow, “On the rate of moment convergence of sample sums and extremes,” Bulletin of the Institute of Mathematics, vol. 16, no. 3, pp. 177–201, 1988. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. W. D. Liu and Z. Y. Lin, “Precise asymptotics for a new kind of complete moment convergence,” Statistics & Probability Letters, vol. 76, no. 16, pp. 1787–1799, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Y.-Y. Chen and L.-X. Zhang, “Second moment convergence rates for uniform empirical processes,” Journal of Inequalities and Applications, vol. 2010, Article ID 972324, 9 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. Z. G. Su, “Precise asymptotics for random matrices and random growth models,” Acta Mathematica Sinica, vol. 24, no. 6, pp. 971–982, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. R. Vershynin, “Introduction to the non-asymptotic analysis of random matrices,” in Compressed Sensing, Y. Eldar and G. Kutyniok, Eds., pp. 210–268, Cambridge University Press, Cambridge, UK, 2012. View at Google Scholar · View at MathSciNet
  12. Z. D. Bai and J. W. Silverstein, Spectral Analysis of Large Dimensional Random Matrices, Science Press, Beijing, China, 2006.
  13. Z. D. Bai, X. Y. Wang, and W. Zhou, “Functional CLT for sample covariance matrices,” Bernoulli, vol. 16, no. 4, pp. 1086–1113, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Z. D. Bai, B. Q. Miao, and J.-F. Yao, “Convergence rates of spectral distributions of large sample covariance matrices,” SIAM Journal on Matrix Analysis and Applications, vol. 25, no. 1, pp. 105–127, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet