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