Introduction to the Mathematical and Statistical Foundations of Econometrics

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9780521542241: Introduction to the Mathematical and Statistical Foundations of Econometrics

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.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Book Description:

'The objective of this book is to use it as an introductory text for a Ph.D. level course in Econometrics. … Appendixes are self contained with review which are easy to learn and understand. As a whole, I consider this book as unique and self-contained and it will be a great resource for researchers in the area of Econometrics.' Zentralblatt MATH

Book Description:

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.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

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1.

Bierens, Herman J.
Editore: CAMBRIDGE UNIVERSITY PRESS, United Kingdom (2004)
ISBN 10: 0521542243 ISBN 13: 9780521542241
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Descrizione libro CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2004. Paperback. Condizione libro: New. 218 x 152 mm. Language: English . Brand New Book. 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. Codice libro della libreria AAU9780521542241

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Bierens, Herman J.
Editore: Cambridge University Press (2004)
ISBN 10: 0521542243 ISBN 13: 9780521542241
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Descrizione libro Cambridge University Press, 2004. Condizione libro: New. This book is intended for use in a rigorous introductory PhD level course in econometrics. Series Editor(s): Phillips, Peter C. B.; Ghysels, Eric; Smith, Richard J. Series: Themes in Modern Econometrics. Num Pages: 344 pages, 19 b/w illus. 12 tables. BIC Classification: KCH. Category: (P) Professional & Vocational. Dimension: 228 x 151 x 19. Weight in Grams: 524. . 2004. Paperback. . . . . . Codice libro della libreria V9780521542241

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Bierens, Herman J.
Editore: Cambridge University Press
ISBN 10: 0521542243 ISBN 13: 9780521542241
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Descrizione libro Cambridge University Press. Paperback. Condizione libro: new. BRAND NEW, Introduction to the Mathematical and Statistical Foundations of Econometrics, Herman J. Bierens, Peter C. B. Phillips, Eric Ghysels, Richard J. Smith, 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. Codice libro della libreria B9780521542241

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4.

Bierens, Herman J.
Editore: CAMBRIDGE UNIVERSITY PRESS, United Kingdom (2004)
ISBN 10: 0521542243 ISBN 13: 9780521542241
Nuovi Paperback Quantità: 1
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Descrizione libro CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2004. Paperback. Condizione libro: New. 218 x 152 mm. Language: English . Brand New Book. 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. Codice libro della libreria AAU9780521542241

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Bierens, Herman J.
Editore: Cambridge University Press 2004-12-20, Cambridge (2004)
ISBN 10: 0521542243 ISBN 13: 9780521542241
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Descrizione libro Cambridge University Press 2004-12-20, Cambridge, 2004. paperback. Condizione libro: New. Codice libro della libreria 9780521542241

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Bierens, Herman J.
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Descrizione libro Cambridge University Press, 2004. Condizione libro: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: 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 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 sigma-algebras; 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 op-notations; 52. Asymptotic normality of M-estimators; 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. Codice libro della libreria ABE_book_new_0521542243

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Descrizione libro Cambridge University Press. Condizione libro: New. This book is intended for use in a rigorous introductory PhD level course in econometrics. Series Editor(s): Phillips, Peter C. B.; Ghysels, Eric; Smith, Richard J. Series: Themes in Modern Econometrics. Num Pages: 344 pages, 19 b/w illus. 12 tables. BIC Classification: KCH. Category: (P) Professional & Vocational. Dimension: 228 x 151 x 19. Weight in Grams: 524. . 2004. Paperback. . . . . Books ship from the US and Ireland. Codice libro della libreria V9780521542241

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Descrizione libro Cambridge University Press, 2004. PAP. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria BB-9780521542241

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Descrizione libro Paperback. Condizione libro: New. Not Signed; 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. book. Codice libro della libreria ria9780521542241_rkm

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Descrizione libro Cambridge University Press, 2004. PAP. Condizione libro: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria LQ-9780521542241

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