## Introduction to the Mathematical and Statistical Foundations of Econometrics by Herman J Bierens pdf free download

Introduction to the Mathematical and Statistical Foundations of Econometrics by Herman J Bierens pdf free download. This book is intended for a rigorous introductory Ph.D. level course in econometrics, or for use in a field course in econometric theory. It is based on lecture notes that I have developed during the period 1997-2003 for the first semester econometrics course “Introduction to Econometrics” in the core of the Ph.D. program in economics at the Pennsylvania State University. Initially these lecture notes were written as a companion to Gallant’s (1997) textbook, but have been developed gradually into an alternative textbook.

### Introduction to the Mathematical and Statistical Foundations of Econometrics by Herman J Bierens pdf free download

Therefore, the topics that are covered in this book encompass those in Gallant’s book, but in much more depth. Moreover, in order to make the book also suitable for a field course in econometric theory I have included various advanced topics as well. I used to teach this advanced material in the econometrics field at the Free University of Amsterdam and Southern Methodist University, on the basis of the draft of my previous textbook, Bierens (1994). Some chapters have their own appendices, containing the more advanced topics and/or

difficult proofs. Moreover, there are three appendices with material that is supposed to be known, but often is not, or not sufficiently. Appendix I contains a comprehensive review of linear algebra, including all the proofs.

#### Introduction to the Mathematical and Statistical Foundations of Econometrics by Herman J Bierens pdf free download

This appendix is intended for self-study only, but may serve well in a half-semester or one quarter course in linear algebra. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews the basics of complex analysis which is needed to understand and derive the properties of characteristic functions. At the beginning of the first class I always tell my students: “Never ask me how. Only ask me why.” In other words, don’t be satisfied with recipes. Of course, this applies to other economics fields as well, in particular if the mission of the Ph.D. program is to place its graduates at research universities.

First, modern economics is highly mathematical. Therefore, in order to be able to make original contributions to economic theory Ph.D. students need to develop a “mathematical mind.” Second, students who are going to work in an applied econometrics field like empirical IO or labor need to be able to read the theoretical econometrics literature in order to keep up-to-date with the latest econometric techniques. Needless to say, students interested in contributing to econometric theory need to become professional mathematicians and statisticians first. Therefore, in this book I focus on teaching “why,” by providing proofs, or at least motivations if proofs are too complicated, of the mathematical and statistical results necessary for understanding modern econometric theory.

Probability theory is a branch of measure theory. Therefore, probability theory is introduced, in Chapter 1, in a measure-theoretical way. The same applies to unconditional and conditional expectations in Chapters 2 and 3, which are introduced as integrals with respect to probability measures. These chapters are also beneficial as preparation for the study of economic theory, in particular modern macroeconomic theory. See for example Stokey, Lucas, and Prescott (1989).

It usually takes me three weeks (at a schedule of two lectures of one hour and fifteen minutes per week) to get through Chapter 1, skipping all the appendices. Chapters 2 and 3 together, without the appendices, usually take me about three weeks as well. Chapter 4 deals with transformations of random variables and vectors, and also lists the most important univariate continuous distributions, together with their expectations, variances, moment generating functions (if they exist), and characteristic functions. I usually explain only the change-of variables formula for (joint) densities, leaving the rest of Chapter 4 for self-tuition.

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