Probability, Statistics and Econometrics - 1st Edition - ISBN: 9780128104958, 9780128104965

Probability, Statistics and Econometrics

1st Edition

Authors: Oliver Linton
eBook ISBN: 9780128104965
Paperback ISBN: 9780128104958
Imprint: Academic Press
Published Date: 3rd March 2017
Page Count: 388
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Description

Probability, Statistics and Econometrics provides a concise, yet rigorous, treatment of the field that is suitable for graduate students studying econometrics, very advanced undergraduate students, and researchers seeking to extend their knowledge of the trinity of fields that use quantitative data in economic decision-making.

The book covers much of the groundwork for probability and inference before proceeding to core topics in econometrics. Authored by one of the leading econometricians in the field, it is a unique and valuable addition to the current repertoire of econometrics textbooks and reference books.

Key Features

  • Synthesizes three substantial areas of research, ensuring success in a subject matter than can be challenging to newcomers
  • Focused and modern coverage that provides relevant examples from economics and finance
  • Contains some modern frontier material, including bootstrap and lasso methods not treated in similar-level books
  • Collects the necessary material for first semester Economics PhD students into a single text

Readership

Very advanced undergraduate and [particularly] graduate students of econometrics, probability and statistics. First semester PhD students. Teachers and researchers in economics and finance

Table of Contents

Part I: Probability and Distribution

Chapter 1: Probability Theory

  • Abstract
  • 1.1. Introduction
  • 1.2. Definition of Probability
  • 1.3. Some Counting Problems
  • References

Chapter 2: Conditional Probability and Independence

  • Abstract
  • 2.1. Conditional Probability
  • 2.2. Bayes Theorem
  • 2.3. Independence
  • References

Chapter 3: Random Variables, Distribution Functions, and Densities

  • Abstract
  • 3.1. Random Variables
  • 3.2. Distribution Functions
  • 3.3. Quantile
  • 3.4. Density and Mass Functions
  • References

Chapter 4: Transformations of Random Variables

  • Abstract
  • 4.1. Distributions of Functions of a Random Variable
  • 4.2. Probability Integral Transform

Chapter 5: The Expectation

  • Abstract
  • 5.1. Definition and Properties
  • 5.2. Additional Moments and Cumulants
  • 5.3. An Interpretation of Expectation and Median
  • References

Chapter 6: Examples of Univariate Distributions

  • Abstract
  • 6.1. Parametric Families of Distributions

Chapter 7: Multivariate Random Variables

  • Abstract
  • 7.1. Multivariate Distributions
  • 7.2. Conditional Distributions and Independence
  • 7.3. Covariance
  • 7.4. Conditional Expectation and the Regression Function
  • 7.5. Examples
  • 7.6. Multivariate Transformations

Chapter 8: Asymptotic Theory

  • Abstract
  • 8.1. Inequalities
  • 8.2. Notions of Convergence
  • 8.3. Laws of Large Numbers and CLT
  • 8.4. Some Additional Tools
  • References

Chapter 9: Exercises and Complements

  • Abstract

Part II: Statistics

Chapter 10: Introduction

  • Abstract
  • 10.1. Sampling Theory
  • 10.2. Sample Statistics
  • 10.3. Statistical Principles
  • References

Chapter 11: Estimation Theory

  • Abstract
  • 11.1. Estimation Methods
  • 11.2. Comparison of Estimators and Optimality
  • 11.3. Robustness and Other Issues with the MLE
  • References

Chapter 12: Hypothesis Testing

  • Abstract
  • 12.1. Hypotheses
  • 12.2. Test Procedure
  • 12.3. Likelihood Tests
  • 12.4. Power of Tests
  • 12.5. Criticisms of the Standard Hypothesis Testing Approach
  • References

Chapter 13: Confidence Intervals and Sets

  • Abstract
  • 13.1. Definitions
  • 13.2. Likelihood Ratio Confidence Interval
  • 13.3. Methods of Evaluating Intervals
  • References

Chapter 14: Asymptotic Tests and the Bootstrap

  • Abstract
  • 14.1. Simulation Methods
  • 14.2. Bootstrap
  • References

Chapter 15: Exercises and Complements

  • Abstract

Part III: Econometrics

Chapter 16: Linear Algebra

  • Abstract
  • 16.1. Matrices
  • 16.2. Systems of Linear Equations and Projection
  • References

Chapter 17: The Least Squares Procedure

  • Abstract
  • 17.1. Projection Approach
  • 17.2. Partitioned Regression
  • 17.3. Restricted Least Squares

Chapter 18: Linear Model

  • Abstract
  • 18.1. Introduction
  • 18.2. The Model

Chapter 19: Statistical Properties of the OLS Estimator

  • Abstract
  • 19.1. Properties of OLS
  • 19.2. Optimality
  • References

Chapter 20: Hypothesis Testing for Linear Regression

  • Abstract
  • 20.1. Hypotheses of Interest
  • 20.2. Test of a Single Linear Hypothesis
  • 20.3. Test of Multiple Linear Hypothesis
  • 20.4. Test of Multiple Linear Hypothesis Based on Fit
  • 20.5. Likelihood Based Testing
  • 20.6. Bayesian Approach

Chapter 21: Omission of Relevant Variables, Inclusion of Irrelevant Variables, and Model Selection

  • Abstract
  • 21.1. Omission of Relevant Variables
  • 21.2. Inclusion of Irrelevant Variables/Knowledge of Parameters
  • 21.3. Model Selection
  • 21.4. Lasso
  • References

Chapter 22: Asymptotic Properties of OLS Estimator and Test Statistics

  • Abstract
  • 22.1. The I.I.D. Case
  • 22.2. The Non-I.I.D. Case
  • References

Chapter 23: Generalized Method of Moments and Extremum Estimators

  • Abstract
  • 23.1. Generalized Method Moments
  • 23.2. Asymptotic Properties of Extremum Estimators
  • 23.3. Quantile Regression
  • References

Chapter 24: A Nonparametric Postscript

  • Abstract
  • References

Chapter 25: A Case Study

  • Abstract

Chapter 26: Exercises and Complements

  • Abstract

Appendix

  • A. Some Results from Calculus
  • B. Some Matrix Facts

Details

No. of pages:
388
Language:
English
Copyright:
© Academic Press 2017
Published:
Imprint:
Academic Press
eBook ISBN:
9780128104965
Paperback ISBN:
9780128104958

About the Author

Oliver Linton

Professor Oliver Linton (Professor of Political Economy, Trinity College, Cambridge University) has been a Co-editor of Econometric Theory since 2000, the Journal of Econometrics since 2014, was Co-Editor of Econometrics Journal from 2007-14. He is an Elected Fellow of the Econometric Society, the Institute of Mathematical Statistics, and the British Academy. He has published over 130 articles in statistics, econometrics, and in empirical finance. He is particularly interested in nonparametric and semiparametric methods and financial econometrics.

Affiliations and Expertise

Professor of Political Economy, Trinity College, Cambridge University, UK