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Introduction to Statistics and Econometrics
Description:
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.
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
Exercises
8. Interval Estimation
8.1 Introduction
8.2 Confidence Intervals
8.3 Bayesian Method
Exercises
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
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