Introduction to the mathematical and statistical foundations of econometrics
 Responsibility
 Herman J. Bierens.
 Imprint
 Cambridge, UK ; New York : Cambridge University Press, 2005.
 Physical description
 1 online resource (xvii, 323 pages) : illustrations
 Series
 Themes in modern econometrics.
Online
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Description
Creators/Contributors
 Author/Creator
 Bierens, Herman J., 1943
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 315316) and index.
 Contents

 Part I. Probability and Measure: 1. The Texas lotto
 2. Quality control
 3. Why do we need sigmaalgebras of events?
 4. Properties of algebras and sigmaalgebras
 5. Properties of probability measures
 6. The uniform probability measures
 7. Lebesque measure and Lebesque integral
 8. Random variables and their distributions
 9. Density functions
 10. Conditional probability, Bayes's rule, and independence
 11. Exercises: A. Common structure of the proofs of Theorems 6 and 10, B. Extension of an outer measure to a probability measure
 Part II. Borel Measurability, Integration and Mathematical Expectations: 12. Introduction
 13. Borel measurability
 14. Integral of Borel measurable functions with respect to a probability measure
 15. General measurability and integrals of random variables with respect to probability measures
 16. Mathematical expectation
 17. Some useful inequalities involving mathematical expectations
 18. Expectations of products of independent random variables
 19. Moment generating functions and characteristic functions
 20. Exercises: A. Uniqueness of characteristic functions
 Part III. Conditional Expectations: 21. Introduction
 22. Properties of conditional expectations
 23. Conditional probability measures and conditional independence
 24. Conditioning on increasing sigmaalgebras
 25. Conditional expectations as the best forecast schemes
 26. Exercises
 A. Proof of theorem 22
 Part IV. Distributions and Transformations: 27. Discrete distributions
 28. Transformations of discrete random vectors
 29. Transformations of absolutely continuous random variables
 30. Transformations of absolutely continuous random vectors
 31. The normal distribution
 32. Distributions related to the normal distribution
 33. The uniform distribution and its relation to the standard normal distribution
 34. The gamma distribution
 35. Exercises: A. Tedious derivations
 B. Proof of theorem 29
 Part V. The Multivariate Normal Distribution and its Application to Statistical Inference: 36. Expectation and variance of random vectors
 37. The multivariate normal distribution
 38. Conditional distributions of multivariate normal random variables
 39. Independence of linear and quadratic transformations of multivariate normal random variables
 40. Distribution of quadratic forms of multivariate normal random variables
 41. Applications to statistical inference under normality
 42. Applications to regression analysis
 43. Exercises
 A. Proof of theorem 43
 Part VI. Modes of Convergence: 44. Introduction
 45. Convergence in probability and the weak law of large numbers
 46. Almost sure convergence, and the strong law of large numbers
 47. The uniform law of large numbers and its applications
 48. Convergence in distribution
 49. Convergence of characteristic functions
 50. The central limit theorem
 51. Stochastic boundedness, tightness, and the Op and opnotations
 52. Asymptotic normality of Mestimators
 53. Hypotheses testing
 54. Exercises: A. Proof of the uniform weak law of large numbers
 B. Almost sure convergence and strong laws of large numbers
 C. Convergence of characteristic functions and distributions
 Part VII. Dependent Laws of Large Numbers and Central Limit Theorems: 55. Stationary and the world decomposition
 56. Weak laws of large numbers for stationary processes
 57. Mixing conditions
 58. Uniform weak laws of large numbers
 59. Dependent central limit theorems
 60. Exercises: A. Hilbert spaces
 Part VIII. Maximum Likelihood Theory
 61. Introduction
 62. Likelihood functions
 63. Examples
 64. Asymptotic properties if ML estimators
 65. Testing parameter restrictions
 66. Exercises.
 (source: Nielsen Book Data)
 Publisher's summary

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 measuretheoretical 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 Mestimators, 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 selfcontained.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2005
 Series
 Themes in modern econometrics
 ISBN
 0511080417 (electronic bk.)
 9780511080418 (electronic bk.)
 0511121695 (electronic bk.)
 9780511121692 (electronic bk.)
 0511079656 (electronic bk. ; Adobe Reader)
 9780511079658 (electronic bk. ; Adobe Reader)
 9780511754012 (ebook)
 0511754019 (ebook)
 9780521834315 (hardback)
 0521834317 (hardback)
 1280163445
 9781280163449
 0521542243 (Paper)
 0521834317 (Cloth)
 9780521542241