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
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
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
Chapter 25: A Case Study
Chapter 26: Exercises and Complements
Appendix
- A. Some Results from Calculus
- B. Some Matrix Facts
