Multivariate Analysis and Jacobi Ensembles: Largest Eigenvalue, Tracy-widom Limits and Rates of Convergence.

  title={Multivariate Analysis and Jacobi Ensembles: Largest Eigenvalue, Tracy-widom Limits and Rates of Convergence.},
  author={Iain M. Johnstone},
  journal={Annals of statistics},
  volume={36 6},
Let A and B be independent, central Wishart matrices in p variables with common covariance and having m and n degrees of freedom, respectively. The distribution of the largest eigenvalue of (A + B)(-1)B has numerous applications in multivariate statistics, but is difficult to calculate exactly. Suppose that m and n grow in proportion to p. We show that after centering and, scaling, the distribution is approximated to second-order, O(p(-2/3)), by the Tracy-Widom law. The results are obtained for… CONTINUE READING
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