作者：Bai, Zhidong; Choi, Kwok Pui; Fujikoshi, Yasunori
作者单位：Northeast Normal University - China; Northeast Normal University - China; National University of Singapore; Hiroshima University
摘要：In this paper, we derive the asymptotic joint distributions of the eigenvalues under the null case and the local alternative cases in the MANOVA model and multiple discriminant analysis when both the dimension and the sample size are large. Our results are obtained by random matrix theory (RMT) without assuming normality in the populations. It is worth pointing out that the null and nonnull distributions of the eigenvalues and invariant test statistics are asymptotically robust against departu...
作者：Gamarnik, David; Li, Quan
作者单位：Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT)
摘要：We consider the problem of finding a k xk submatrix of an nxn matrix with i.i.d. standard Gaussian entries, which has a large average entry. It was shown in [Bhamidi, Dey and Nobel (2012)] using nonconstructive methods that the largest average value of a k x k submatrix is 2(1 + o(1)) root log n/k, with high probability (w.h.p.), when k = O(log n/log log n). In the same paper, evidence was provided that a natural greedy algorithm called the Largest Average Submatrix (LAS) for a constant k shou...
