Probability, Statistics and Econometrics provides a concise, yet rigorous, treatment of the field that is suitable for graduate students studying econometrics, very advanced undergraduate students, and researchers seeking to extend their knowledge of the trinity of fields that use quantitative data in economic decision-making.
The book covers much of the groundwork for probability and inference before proceeding to core topics in econometrics. Authored by one of the leading econometricians in the field, it is a unique and valuable addition to the current repertoire of econometrics textbooks and reference books.
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
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