"Introduction to Statistics and Econometrics covers probability and statistics, with emphasis on certain
topics that are important in econometrics but often overlooked by statistics textbooks at this level...A thorough
analysis of the problem of choosing estimators is given, including a comparison of various criteria for ranking
estimators. The author also presents a critical evaluation of the classical method of hypothesis testing, especially
in the realistic case of testing two composite hypothesis against each other."
--Quarterly Journal of Applied Mathematics
Harvard University Press Web Site, December, 2003
Summary
This outstanding text by a foremost econometrician combines instruction in probability and statistics with econometrics
in a rigorous but relatively nontechnical manner. Unlike many statistics texts, it discusses regression analysis
in depth. And unlike many econometrics texts, it offers a thorough treatment of statistics. Although its only mathematical
requirement is multivariate calculus, it challenges the student to think deeply about basic concepts.
The coverage of probability and statistics includes best prediction and best linear prediction, the joint distribution
of a continuous and discrete random variable, large sample theory, and the properties of the maximum likelihood
estimator. Exercises at the end of each chapter reinforce the many illustrative examples and diagrams. Believing
that students should acquire the habit of questioning conventional statistical techniques, Takeshi Amemiya discusses
the problem of choosing estimators and compares various criteria for ranking them. He also evaluates classical
hypothesis testing critically, giving the realistic case of testing a composite null against a composite alternative.
He frequently adopts a Bayesian approach because it provides a useful pedagogical framework for discussing many
fundamental issues in statistical inference.
Turning to regression, Amemiya presents the classical bivariate model in the conventional summation notation. He
follows with a brief introduction to matrix analysis and multiple regression in matrix notation. Finally, he describes
various generalizations of the classical regression model and certain other statistical models extensively used
in econometrics and other applications in social science.
Table of Contents
Preface
1. Introduction
1.1 What Is Probability?
1.2 What Is Statistics?
2. Probability
2.1 Introduction
2.2 Axioms of Probability
2.3 Counting Techniques
2.4 Conditional Probability and Independence
2.5 Probability Calculations
Exercises
3. Random Variables And Probability Distributions
3.1 Definitions of a Random Variable
3.2 Discrete Random Variables
3.3 Univariate Continuous Random Variables
3.4 Bivariate Continuous Random Variables
3.5 Distribution Function
3.6 Change of Variables
3.7 Joint Distribution of Discrete and Continuous Random Variables
Exercises
4. Moments
4.1 Expected Value
4.2 Higher Moments
4.3 Covariance and Correlation
4.4 Conditional Mean and Variance
Exercises
5. Binomial And Normal Random Variables
5.1 Binomial Random Variables
5.2 Normal Random Variables
5.3 Bivariate Normal Random Variables
5.4 Multivariate Normal Random Variables
Exercises
6. Large Sample Theory
6.1 Modes of Convergence
6.2 Laws of Large Numbers and Central Limit Theorems
6.3 Normal Approximation of Binomial
6.4 Examples
Exercises
7. Point Estimation
7.1 What Is an Estimator?
7.2 Properties of Estimators
7.3 Maximum Likelihood Estimator: Definition and Computation
7.4 Maximum Likelihood Estimator: Properties
9. Tests Of Hypotheses
9.1 Introduction
9.2 Type I and Type II Errors
9.3 Neyman-Pearson Lemma
9.4 Simple against Composite
9.5 Composite against Composite
9.6 Examples of Hypothesis Tests
9.7 Testing about a Vector Parameter
Exercises
10. Bivariate Regression Model
10.1 Introduction
10.2 Least Squares Estimators
10.3 Tests of Hypotheses
Exercises
11. Elements Of Matrix Analysis
11.1 Definition of Basic Terms
11.2 Matrix Operations
11.3 Determinants and Inverses
11.4 Simultaneous Linear Equations
11.5 Properties of the Symmetric Matrix
Exercises
12. Multiple Regression Model
12.1 Introduction
12.2 Least Squares Estimators
12.3 Constrained Least Squares Estimators
12.4 Tests of Hypotheses
12.5 Selection of Regressors
Exercises
13. Econometric Models
13.1 Generalized Least Squares
13.2 Time Series Regression
13.3 Simultaneous Equations Model
13.4 Nonlinear Regression Model
13.5 Qualitative Response Model
13.6 Censored or Truncated Regression Model (Tobit Model)
13.7 Duration Model
Appendix: Distribution Theory
References
Name Index
Subject Index
