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.
Key Features
- Synthesizes three substantial areas of research, ensuring success in a subject matter than can be challenging to newcomers
- Focused and modern coverage that provides relevant examples from economics and finance
- Contains some modern frontier material, including bootstrap and lasso methods not treated in similar-level books
- Collects the necessary material for first semester Economics PhD students into a single text
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
- Smith, Essential Statistics, Regression and Econometrics, 2015, 9780128034590, 396pp, $110.00
- Ross, Introductory Statistics, 2013, 9780123743886, 848pp, $109.95
- Heckman and Learner, Handbook of Econometrics 6A, 2008, North Holland, 9780444506313, 1032pp, $180.00
- Heckman and Learner, Handbook of Econometrics 6B, 2008, North Holland, 9780444532008, 1056pp, $180.00
