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《计量经济学的数学和统计学基础》2005年出版

Introduction to the Mathematical and Statistical Foundations of Econometrics

Cambridge University Press 2005

Herman J. Bierens

Pennsylvania State University

Introduction

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, and 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 appendixes containing more advanced topics and/or difficult proofs. Moreover, there are three appendixes with material that is supposed to be known. Appendix I contains a comprehensive reviewof 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.

Herman J. Bierens is Professor of Economics at the Pennsylvania State University and part-time Professor of Econometrics at Tilburg University, The Netherlands. He is Associate Editor of the Journal of Econometrics and Econometric Reviews, and has been an Associate Editor of Econometrica. Professor Bierens has written two monographs, Robust Methods and Asymptotic Theory in Nonlinear Econometrics and Topics in Advanced Econometrics (Cambridge University Press 1994), as well as numerous journal articles. His current research interests are model (mis)specification analysis in econometrics and its application in empirical research, time series econometrics, and the econometric analysis of dynamic stochastic general equilibrium models.

Contents

1 Probability and Measure 1

2 Borel Measurability, Integration, and Mathematical Expectations 37

3 Conditional Expectations 66

4 Distributions and Transformations 86

5 The Multivariate Normal Distribution and Its Application to Statistical Inference 110

6 Modes of Convergence 137

7 Dependent Laws of Large Numbers and Central Limit Theorems 179

8 Maximum Likelihood Theory 205

Appendix

I Review of Linear Algebra 229

II Miscellaneous Mathematics 283

III A Brief Review of Complex Analysis 298

IV Tables of Critical Values 306

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