By Zehua Chen, Jin-ting Zhang, Feifang Hu

ISBN-10: 9812793089

ISBN-13: 9789812793089

ISBN-10: 9812793097

ISBN-13: 9789812793096

This booklet, that is break up into components, is ready Prof. Zhidong Bai's lifestyles and his contributions to statistical data and chance. 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 components of random matrix conception, Edgeworth enlargement, M-estimation, version choice, adaptive layout in scientific trials, utilized likelihood in algorithms, small sector estimation, and time sequence, between others. This e-book offers a simple entry to Zhidong Bai's very important works, and serves as an invaluable reference for researchers who're operating within the suitable parts.

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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

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29 3. Delayed Responses In practice, the responses are usually not available immediately. We call this delayed responses. There is no logistical difficulty in incorporating delayed responses into urn model. One can just update the urn when responses become available (Hu and Rosenberger, 2006). Bai, Hu and Rosenberger (2002) were the first t o explore the effects of delayed responses theoretically. They proposed a very general framework for delayed response under the generalized Friedman’s urn. T h e delay mechanism can depend on the patient’s entry time, treatment assignment, and response.

Annals of Applied Probability, 12, 1149-1173 (2002). 31 PROFESSOR BAI’S CONTRIBUTIONS TO M-ESTIMATION Y . ca M-estimation, as a generalization of maximum likelihood estimation, plays an important and complementary role in robust statistics. Dr. Bai has made prestigious contributions t o this area. In this article, as a coauthor and good friend, I will describe some of his major contributions. 1. Introduction It is often that the underlying distribution of data is not exactly as assumed and/or the data are subject to error from various sources with complex or un-expressible likelihood functions.

Limits of extreme eigenvalues During his Pittsburgh period, Bai investigated the problem of limits of extreme eigenvalues of the sample covariance S,. Very few was known on the problem at that time: indeed Geman (1980) proved that Amax(Sn) converges almost surely to a2(1 where o2 = E [ I X ~ Iis~the ~ ]common variance of the observed variables and y > 0 is the limit of column-row ratio p / n , under a restriction on the growth of the moments : for each k, E[IX11lk]5 kak for some constant a. 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.

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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


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