Probability, Statistics and Econometrics

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