Introduction to the Mathematical and Statistical Foundations of Econometrics

Herman J. Bierens

• Editore: Cambridge University Press
• Anno: 2004
• ISBN:
  9780511078897
• Argomento: Economía
• Categoria: Econometría

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.

Indice dei contenuti

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