Introduction to the Mathematical and Statistical Foundations of Econometrics

Herman J. Bierens

Pennsylvania State University

• Contents and Preface
• Chapter 1: Probability and Measure
• Chapter 2: Borel Measurability, Integration, and Mathematical Expectations
• Chapter 3: Conditional Expectations
• Chapter 4: Distributions and Transformations
• Chapter 5: The Multivariate Normal Distribution and its Application to Statistical Inference
• Chapter 6: Modes of Convergence
• Chapter 7: Dependent Laws of Large Numbers and Central Limit Theorems
• Chapter 8: Maximum Likelihood Theory
• Appendix I: Review of Linear Algebra
• Appendix II: Miscellaneous Mathematics
• Appendix III: A Brief Review of Complex Analysis
• Appendix IV: Tables of Critical Values
• References

1. Errata to the first (2004) edition
   (These errors have been corrected in the 2007 reprint of the paper back edition)
2. Remaining errors in both editions:
   • Errata and improvements [Updated: January 26, 2012]
   • The Wold decompostion [Updated: February 1, 2012]

1. Rachida Ouysse (2006), Economic Record 82, 230-231
   Concluding remarks:

   Overall, this is an excellent textbook. It offers a unique perspective different from the standard approach in the mainstream textbooks. It encourages the mastering of fundamental concepts and theoretical perspectives at a formal level geared to develop a 'mathematical mind'. It will prove valuable not only for graduate students in econometrics and econometric theory but also as a reference to all researchers in modern economics, econometrics, statistics and financial econometrics.

2. James Davidson (2007), Econometric Reviews 26, 605-607
   Concluding remarks:

   One outstanding virtue of Bierens' book is the inclusion of a large number of proofs. Some are in the text, and some are relegated to chapter appendices, but in any case, these are an essential ingredient of any such text.... Taken as a whole, this book can be seen as a rather personal compendium of things that Professor Bierens regards as important for students to know. It would be difficult indeed to fit more bits of knowledge useful to the apprentice econometrician into a book of this compass. It represents both an outstanding investment for the graduate student and an item that many researchers and practitioners will find invaluable for reference.

1. I have been searching for a real solid introduction to statistics for a long time. And this book is the most in-depth yet readable book so far. It covers advanced topics in statistics such as the F and t distribution formulas, the convergence theorems, the sigma-algebra, and knowledge in matrix, where there is a whole section on determinants!
   If you are a serious student in Statistics, Econometrics or Quantitative Finance, I suggest you must have this book along with you as "what-is" reference, since most schools nowadays bypass these fundamental knowledge in courses and hinder your understanding of the whole structure.

2. This book is a very well written introduction to the probability and measure foundations of econometrics. It provides a good balance between rigor and intuition. I believe that everyone interested in this subject should read this book, since it provides the necessary tools to understand the language and the tools necessary to understand papers in this field.