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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.

### Details & Specs

The following ISBNs are associated with this title:

ISBN - 10:0674462254

ISBN - 13:9780674462250

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### Extra Content

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

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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