Topics In Random Matrices And Statistical Machine Learning

Abstract

This thesis consists of two independent parts: random matrices, which form the first one-third of this thesis, and machine learning, which constitutes the remaining part. The main results of this thesis are as follows: a necessary and sufficient condition for the inverse moments of \((m,n,\beta)\)-Laguerre matrices and compound Wishart matrices to be finite; the universal weak consistency and the strong consistency of the \(k\)-nearest neighbor rule in metrically sigma-finite dimensional spaces and metrically finite dimensional spaces respectively. In Part I, the Chapter 1 introduces the \((m,n,\beta)\)-Laguerre matrix, Wishart and compound Wishart matrix and their joint eigenvalue distribution. While in Chapter 2, a necessary and sufficient condition to have finite inverse moments has been derived. In Part II, the Chapter 1 introduces the various notions of metric dimension and differentiation property followed by our proof for the necessary part of Preiss' result. Further, Chapter 2

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