Introduction to the Mathematical and Statistical Foundations of Econometrics [Hardcover]

This book is intended for use in a rigorous introductory PhD level course in econometrics.This book is intended to be used in a first-semester Ph.D. level course in econometrics, but because it contains much advanced material, particularly in the appendices to the chapters, it is also suitable for a field course in econometric theory. The focus of this book is on understanding why rather than how the mathematical and statistical foundations of econometrics are established. Therefore, the text provides all the proofs, or at least motivations if proofs are too complicated, of the mathematical and statistical results necessary for understanding modern econometric theory. In this respect it differs from all other econometrics textbooks.This book is intended to be used in a first-semester Ph.D. level course in econometrics, but because it contains much advanced material, particularly in the appendices to the chapters, it is also suitable for a field course in econometric theory. The focus of this book is on understanding why rather than how the mathematical and statistical foundations of econometrics are established. Therefore, the text provides all the proofs, or at least motivations if proofs are too complicated, of the mathematical and statistical results necessary for understanding modern econometric theory. In this respect it differs from all other econometrics textbooks.The focus of this book is on clarifying the mathematical and statistical foundations of econometrics. Therefore, the text provides all the proofs, or at least motivations if proofs are too complicated, of the mathematical and statistical results necessary for understanding modern econometric theory. In this respect, it differs from other econometrics textbooks.Part I. Probability and Measure: 1. The Texas lotto; 2. Quality control; 3. Why do we need sigma-algebras of events?; 4. Properties of algebras and sigma-algebras; 5. Properties of probability measures; 6. The uniform probability measureló