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 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