Anindya Roy – författare

Linear Algebra and Matrix Analysis for Statistics offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book is as self-contained as possible, assuming no prior knowledge of linear algebra.The authors first address the rudimentary mechanics of linear systems using Gaussian elimination and the resulting decompositions. They introduce Euclidean vector spaces using less abstract concepts and make connections to systems of linear equations wherever possible. After illustrating the importance of the rank of a matrix, they discuss complementary subspaces, oblique projectors, orthogonality, orthogonal projections and projectors, and orthogonal reduction.The text then shows how the theoretical concepts developed are handy in analyzing solutions for linear systems. The authors also explain how determinants are useful for characterizing and deriving properties concerning matrices and linear systems. They then cover eigenvalues, eigenvectors, singular value decomposition, Jordan decomposition (including a proof), quadratic forms, and Kronecker and Hadamard products. The book concludes with accessible treatments of advanced topics, such as linear iterative systems, convergence of matrices, more general vector spaces, linear transformations, and Hilbert spaces.

Assuming no prior knowledge of linear algebra, this self-contained text offers a gradual exposition to linear algebra without sacrificing the rigor of the subject. It presents both the vector space approach and the canonical forms in matrix theory. The book covers important topics in linear algebra that are useful for statisticians, including the concept of rank, the fundamental theorem of linear algebra, projectors, and quadratic forms. It also provides an extensive collection of exercises on theoretical concepts and numerical computations.

This book addresses a diverse set of topics of contemporary interest in statistics and data science such as biostatistics and machine learning. Each chapter provides an overview of the topic under discussion, so that any reader with an understanding of graduate-level statistics, but not necessarily with a prior background on the topic should be able to get a summary of developments in the field. These chapters serve as basic introductory references for new researchers in these fields, as well as the basis of teaching a course on the topic, or with a part of the course on topics of precision medicine, deep learning, high-dimensional central limit theorems, multivariate rank testing, R programming for statistics, Bayesian nonparametrics, large deviation asymptotics, spatio-temporal modeling of Covid-19, statistical network models, hidden Markov models, statistical record linkage analysis. The edited volume will be most useful for graduate students looking for an overview of any of the covered topics for their research and for instructors for developing certain courses by including any of the topics as part of the course. Students enrolled in a course covering any of the included topics can also benefit from these chapters.