By Zehua Chen, Jin-ting Zhang, Feifang Hu
This ebook, that's cut up into components, is set Prof. Zhidong Bai's existence and his contributions to stats and likelihood. the 1st half includes an interview with Zhidong Bai performed through Dr Atanu Biswas from the Indian Statistical Institute, and 7 brief articles detailing Bai's contributions. the second one half is a set of his chosen seminal papers within the parts of random matrix concept, Edgeworth enlargement, M-estimation, version choice, adaptive layout in scientific trials, utilized likelihood in algorithms, small zone estimation, and time sequence, between others. This publication presents a simple entry to Zhidong Bai's very important works, and serves as an invaluable reference for researchers who're operating within the appropriate parts.
Read Online or Download Advances in Statistics: Proceedings of the Conference in Honor of Professor Zhidong Bai on His 65th Birthday, National University of Singapore, 20 July 2008 PDF
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Extra info for Advances in Statistics: Proceedings of the Conference in Honor of Professor Zhidong Bai on His 65th Birthday, National University of Singapore, 20 July 2008
A major achievement on the problem was made by Yin, Bai and Krishnaiah (1988) where the above convergence of, , ,A ( S n ) was established without Geman’s restrictive assumption and assuming E[/X11l4]< 00 only. This result is indeed optimal: actually in Bai, Silverstein and Yin (1988), the authors proved that almost surely, limsup,A,,,(S,) = 00 if E[IX11I4]= 00. On the other hand, for the smallest + 39 eigenvalue X m i n ( S n ) , its convergence to the left edge a2(1- 4)'(assuming y < 1) is also established in Bai and Yin (1993).
Note that Assumption 2 may not hold even under CramBr’s condition. In that sense t,he results do not completely cover the caw considered by Bhattaoharya and Ghosh (1978), just a8 the main result of Bai and Rao (1991) does not completely extend the results knowa under the usual Cramer’s condition. In thie papel! we establish the following two main theorems. Without loss of generality, we can assume that p = 0 and H ( p ) = 0. Theorem 1. r5uppose Aaauqtions 1, a, and 3 hold with q(m) = m-1. Then we have lIFfi--~dl = gulp I Fn(4-@mn(4l = o(n-(m-a)/a).
Throughout this paper, we assume that p is a nonmonotonic convex function, and is a non-trivial nondecreasing function, and that p is fixed as n -+ 00. Write $J s, = c x i x ; , d: = max xiS;‘xi. I
Advances in Statistics: Proceedings of the Conference in Honor of Professor Zhidong Bai on His 65th Birthday, National University of Singapore, 20 July 2008 by Zehua Chen, Jin-ting Zhang, Feifang Hu