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© 2020

Matrix-Based Introduction to Multivariate Data Analysis

Textbook

Table of contents

  1. Front Matter
    Pages i-xix
  2. Elementary Statistics with Matrices

    1. Front Matter
      Pages 1-1
    2. Kohei Adachi
      Pages 3-16
    3. Kohei Adachi
      Pages 17-29
    4. Kohei Adachi
      Pages 31-45
  3. Least Squares Procedures

    1. Front Matter
      Pages 47-47
    2. Kohei Adachi
      Pages 49-64
    3. Kohei Adachi
      Pages 65-80
    4. Kohei Adachi
      Pages 81-94
    5. Kohei Adachi
      Pages 95-107
  4. Maximum Likelihood Procedures

    1. Front Matter
      Pages 109-109
    2. Kohei Adachi
      Pages 131-148
    3. Kohei Adachi
      Pages 149-163
    4. Kohei Adachi
      Pages 165-177
    5. Kohei Adachi
      Pages 179-194
  5. Miscellaneous Procedures

    1. Front Matter
      Pages 195-195
    2. Kohei Adachi
      Pages 197-209
    3. Kohei Adachi
      Pages 229-245

About this book

Introduction

This is the first textbook that allows readers who may be unfamiliar with matrices to understand a variety of multivariate analysis procedures in matrix forms. By explaining which models underlie particular procedures and what objective function is optimized to fit the model to the data, it enables readers to rapidly comprehend multivariate data analysis. Arranged so that readers can intuitively grasp the purposes for which multivariate analysis procedures are used, the book also offers clear explanations of those purposes, with numerical examples preceding the mathematical descriptions.

Supporting the modern matrix formulations by highlighting singular value decomposition among theorems in matrix algebra, this book is useful for undergraduate students who have already learned introductory statistics, as well as for graduate students and researchers who are not familiar with matrix-intensive formulations of multivariate data analysis.

The book begins by explaining fundamental matrix operations and the matrix expressions of elementary statistics. Then, it offers an introduction to popular multivariate procedures, with each chapter featuring increasing advanced levels of matrix algebra.

Further the book includes in six chapters on advanced procedures, covering advanced matrix operations and recently proposed multivariate procedures, such as sparse estimation, together with a clear explication of the differences between principal components and factor analyses solutions. In a nutshell, this book allows readers to gain an understanding of the latest developments in multivariate data science.


Keywords

Statistics Multivariate Analysis Data Analysis Matrices Vectors Sparse Estimation

Authors and affiliations

  1. 1.Graduate School of Human SciencesOsaka UniversitySuitaJapan

About the authors

Kohei Adachi, Graduate School of Human Sciences, Osaka University

Bibliographic information

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