*James Davidson*

- Published in print:
- 1994
- Published Online:
- November 2003
- ISBN:
- 9780198774037
- eISBN:
- 9780191596117
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774036.001.0001
- Subject:
- Economics and Finance, Econometrics

This book aims to introduce modern asymptotic theory to students and practitioners of econometrics. It falls broadly into two parts. The first half provides a handbook and reference for the ...
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This book aims to introduce modern asymptotic theory to students and practitioners of econometrics. It falls broadly into two parts. The first half provides a handbook and reference for the underlying mathematics (Part I, Chapters 1‐6), statistical theory (Part II, Chapters 7‐11) and stochastic process theory (Part III, Chapters 12‐17). The second half provides a treatment of the main convergence theorems used in analysing the large sample behaviour of econometric estimators and tests. These are the law of large numbers (Part IV, Chapters 18‐21), the central limit theorem (Part V, Chapters 22‐25) and the functional central limit theorem (Part VI, Chapters 26‐30). The focus in this treatment is on the nonparametric approach to time series properties, covering topics such as nonstationarity, mixing, martingales, and near‐epoch dependence. While the approach is not elementary, care is taken to keep the treatment self‐contained. Proofs are provided for almost all the results.Less

This book aims to introduce modern asymptotic theory to students and practitioners of econometrics. It falls broadly into two parts. The first half provides a handbook and reference for the underlying mathematics (Part I, Chapters 1‐6), statistical theory (Part II, Chapters 7‐11) and stochastic process theory (Part III, Chapters 12‐17). The second half provides a treatment of the main convergence theorems used in analysing the large sample behaviour of econometric estimators and tests. These are the law of large numbers (Part IV, Chapters 18‐21), the central limit theorem (Part V, Chapters 22‐25) and the functional central limit theorem (Part VI, Chapters 26‐30). The focus in this treatment is on the nonparametric approach to time series properties, covering topics such as nonstationarity, mixing, martingales, and near‐epoch dependence. While the approach is not elementary, care is taken to keep the treatment self‐contained. Proofs are provided for almost all the results.

*James Davidson*

- Published in print:
- 1994
- Published Online:
- November 2003
- ISBN:
- 9780198774037
- eISBN:
- 9780191596117
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774036.003.0004
- Subject:
- Economics and Finance, Econometrics

The concept of an abstract integral is developed from first principles. Riemann‐Stieltjes and Lebesgue‐Stieltjes integrals are defined. The monotone convergence theorem, fundamental properties of ...
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The concept of an abstract integral is developed from first principles. Riemann‐Stieltjes and Lebesgue‐Stieltjes integrals are defined. The monotone convergence theorem, fundamental properties of integrals, and related inequalities are covered. Other topics include product measure and multiple integrals, Fubini's theorem, signed measures, and the Radon‐Nikodym theorem.Less

The concept of an abstract integral is developed from first principles. Riemann‐Stieltjes and Lebesgue‐Stieltjes integrals are defined. The monotone convergence theorem, fundamental properties of integrals, and related inequalities are covered. Other topics include product measure and multiple integrals, Fubini's theorem, signed measures, and the Radon‐Nikodym theorem.

*Brian Skyrms*

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199652808
- eISBN:
- 9780191745829
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199652808.003.0011
- Subject:
- Philosophy, Philosophy of Science, Metaphysics/Epistemology

Does radical probabilism have enough structure to say anything interesting? Structure is provided by coherent belief change. Coherence imposes the Martingale property, which gives convergence ...
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Does radical probabilism have enough structure to say anything interesting? Structure is provided by coherent belief change. Coherence imposes the Martingale property, which gives convergence theorems and theorems about the value of knowledge.Less

Does radical probabilism have enough structure to say anything interesting? Structure is provided by coherent belief change. Coherence imposes the Martingale property, which gives convergence theorems and theorems about the value of knowledge.

*Fon-Che Liu*

- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780198790426
- eISBN:
- 9780191831676
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198790426.003.0002
- Subject:
- Mathematics, Analysis

A glimpse of measure and integration is provided for the reader to have an early overall view of the subject. The important space of all functions f with integrable p-th power of |f| is also ...
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A glimpse of measure and integration is provided for the reader to have an early overall view of the subject. The important space of all functions f with integrable p-th power of |f| is also introduced in this chapter to provide the reader with an early appreciation of the power of convergence theorems of the theory which, together with the Egoroff theorem, reveal convincingly the role of sigma-additivity of measure in making measure theory a useful tool in analysis. Various types of families of sets and set functions defined on them are studied for later use in this chapter as well as in following chapters. With the introduction of measure space, and with simple functions taking the role of step functions in the definition of Riemann integral, the definition of integral within the framework of measure space becomes natural and straightforward, and leads to a theory surprisingly powerful and rich in structure.Less

A glimpse of measure and integration is provided for the reader to have an early overall view of the subject. The important space of all functions f with integrable p-th power of |f| is also introduced in this chapter to provide the reader with an early appreciation of the power of convergence theorems of the theory which, together with the Egoroff theorem, reveal convincingly the role of sigma-additivity of measure in making measure theory a useful tool in analysis. Various types of families of sets and set functions defined on them are studied for later use in this chapter as well as in following chapters. With the introduction of measure space, and with simple functions taking the role of step functions in the definition of Riemann integral, the definition of integral within the framework of measure space becomes natural and straightforward, and leads to a theory surprisingly powerful and rich in structure.