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Title: Central Limit Theorem of Linear Spectral Statistics for Large Dimensional Random Matrices
Keywords: Central limit theorem, linear spectral statistics, large dimensional random matrices, Wigner matrix, sample covariance matrix
Issue Date: 4-Jun-2009
Citation: WANG XIAOYING (2009-06-04). Central Limit Theorem of Linear Spectral Statistics for Large Dimensional Random Matrices. ScholarBank@NUS Repository.
Abstract: With the development of computer science, large dimensional data have become increasingly common in various disciplines. These data resist conventional multivariate analysis that relies on large sample theory, since the number of variables for each observation can be very large and even comparable to the sample size. Consequently, a new approach, large dimensional random matrices theory, has been proposed to replace the classical large sample theory.The limiting distributions of the linear spectral statistics of large dimensional random matrices play an important role in large dimensional data analysis. In this thesis, using the Bernstein polynomial approximation and Stieltjes transform method, we prove the central limit theorem of linear spectral statistics with a generalized regular class C4 of the test functions for large dimensional Wigner matrices and sample covariance matrices.
Appears in Collections:Ph.D Theses (Open)

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