Matrix Differential Calculus with Applications in Statistics and Econometrics

Jan R. Magnus, Heinz Neudecker

• Publisher: Wiley
• Year: 2019
• Print ISBN: 9781119541202
• eBook ISBN: 9781119541165
• Edition: 3
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

A brand new, fully updated edition of a popular classic on matrix differential calculus with applications in statistics and econometrics

This exhaustive, self-contained book on matrix theory and matrix differential calculus provides a treatment of matrix calculus based on differentials and shows how easy it is to use this theory once you have mastered the technique. Jan Magnus, who, along with the late Heinz Neudecker, pioneered the theory, develops it further in this new edition and provides many examples along the way to support it.

Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioral sciences to econometrics. It is still relevant and used today in a wide range of subjects such as the biosciences and psychology. Matrix Differential Calculus with Applications in Statistics and Econometrics, Third Edition contains all of the essentials of multivariable calculus with an emphasis on the use of differentials. It starts by presenting a concise, yet thorough overview of matrix algebra, then goes on to develop the theory of differentials. The rest of the text combines the theory and application of matrix differential calculus, providing the practitioner and researcher with both a quick review and a detailed reference.

• Fulfills the need for an updated and unified treatment of matrix differential calculus
• Contains many new examples and exercises based on questions asked of the author over the years
• Covers new developments in field and features new applications
• Written by a leading expert and pioneer of the theory
• Part of the Wiley Series in Probability and Statistics

Matrix Differential Calculus With Applications in Statistics and Econometrics Third Edition is an ideal text for graduate students and academics studying the subject, as well as for postgraduates and specialists working in biosciences and psychology.

Part One
Matrices

Chapter 1
Basic properties of vectors and matrices

1 INTRODUCTION

In this chapter, we summarize some of the well‐known definitions and theorems of matrix algebra. Most of the theorems will be proved.

2 SETS

A set is a collection of objects, called the elements (or members) of the set. We write x ∈ S to mean ‘x is an element of S’ or ‘x belongs to S’. If x does not belong to S, we write x ∉ S. The set that contains no elements is called the empty set, denoted by ∅.

Sometimes a set can be defined by displaying the elements in braces. For example, A = {0, 1} or

Notice that A is a finite set (contains a finite number of elements), whereas ℕ is an infinite set. If P is a property that any element of S has or does not have, then

denotes the set of all the element...

Table of contents

• Cover
• Table of Contents
• Preface
• Part One: Matrices
• Part Two: Differentials: the theory
• Part Three: Differentials: the practice
• Part Four: Inequalities
• Part Five: The linear model
• Part Six: Applications to maximum likelihood estimation
• Part Seven: Summary
• Bibliography
• Index of symbols
• Subject index
• End User License Agreement