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Probability, Statistics and Econometrics

Oliver Linton
Publisher: 
Academic Press
Publication Date: 
2017
Number of Pages: 
367
Format: 
Paperback
Price: 
99.95
ISBN: 
9780128104958
Category: 
Textbook
We do not plan to review this book.

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