Introduction to the Mathematical and Statistical Foundations of Econometrics (Themes in Modern Econometrics)

This textbook provides a systematic survey of the most recent developments in input-output analysis and their applications, helping us to examine questions such as: Which industries are competitive? What are the multiplier effects of an investment program? How do environmental restrictions impact on prices? Linear programming and national accounting are introduced and used to resolve issues such as the choice of technique, the comparative advantage of a national economy, its efficiency and dynamic performance. Technological and environmental spillovers are analyzed, both at the national level (between industries) and the international level (the measurement of globalization effects) Probability and measure -- Borel measurability, integration, and mathematical expectations -- Conditional expectations -- Distributions and transformations -- The multivariate normal distribution and its application to statistical inference -- Modes of convergence -- Dependent laws of large numbers and central limit theorems -- Maximum likelihood theory This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory. It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory. 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. Appendix I contains a comprehensive review of linear algebra, including all the proofs. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews complex analysis. Therefore, this book is uniquely self-contained. This Book Is Intended For Use In A Rigorous Introductory Ph.d.-level Course In Econometrics, Or In A Field Course In Econometric Theory. It Covers The Measure - Theoretical Foundation Of Probability Theory, The Multivariate Normal Distribution With Its Application To Classical Linear Regression Analysis, Various Laws Of Large Numbers, Central Limit Theorems And Related Results For Independent Random Variables As Well As For Stationary Time Series, With Applications To Asymptotic Inference Of M-estimators, And Maximum Likelihood Theory.--book Jacket. Probability And Measure -- Borel Measurability, Integration, And Mathematical Expectations -- Conditional Expectations -- Distributions And Transformations -- The Multivariate Normal Distribution And Its Application To Statistical Inference -- Modes Of Convergence -- Dependent Laws Of Large Numbers And Central Limit Theorems -- Maximum Likelihood Theory. Herman J. Bierens. Includes Bibliographical References And Index. "This book is intended for use in a rigorous introductory Ph. D.-level course in econometrics, or in a field course in econometric theory. It covers the measure - theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory."--Jacket 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. Intended for use in a rigorous introductory PhD level course in econometrics, or a field course in econometric theory, this book covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, and more