By Zehua Chen, Jin-ting Zhang, Feifang Hu
This publication, that's break 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 carried out 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 idea, Edgeworth growth, M-estimation, version choice, adaptive layout in medical trials, utilized likelihood in algorithms, small quarter estimation, and time sequence, between others. This ebook presents a simple entry to Zhidong Bai's vital works, and serves as an invaluable reference for researchers who're operating within the suitable parts.
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Extra resources 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
Pn(yn,P), . } be a sequence of dispersion functions which are differentiable about P for almost all y's, where 51 is an open convex subset of RP known as the parameter space. Then the general M-estimate is defined as any value of P minimizing fl n i=l Let t,bi(yi,p) denote the derivative of pi(yi,p ) about 0 otherwise. Then, satisfies P if the derivative exists and n i=l if the left side of (7) is continuous at P, or otherwise. Assume that there exists a vector Po E R and for each i there are an nonnegative definite matrix Gi and a function q i ( P ) such that with q i ( p ) = o(Qi(P-Po)) as P + Po, where Qi is some nonnegative definite matrix.
Krishnaiah in Pittsburgh. d. standardized complex-valued random variables so that the sample covariance matrix is defined as S, = n-’X,X;. In a series of papers, see Yin, Bai and Krishnaiah (1983), Bai, Yin and Krishnaiah (1986, 1987), Bai and Yin (1986), the existence of a LSD is proved for products A, = S,T, of S, with an independent and positive definite Hermitian matrix Tn. This class of RM’s includes the widely-used F-matrix in multivariate data analysis. W. Silverstein on the class of generalised sample covariance matrices.
Bai, Z. D. and Krishnaiah, P. , On the limit of the largest eigenvalue of the large-dimensional sample covariance matrix, Probab. Theory Related Fields, 78,509521,( 1988). 23. Bai, Z. , Yin, Y. Q . and Krishnaiah, P. , On limiting empirical distribution function of the eigenvalues of a multivariate F matrix, Teor. Veroyatnost. , 32,537-548,( 1987). 24. Bai, Z. , Krishnaiah, P. R. and Liang, W. , On asymptotic joint distribution of the eigenvalues of the noncentral MANOVA matrix for nonnormal populations, Sankhyd Ser.