Introduction to Statistics and Econometrics

by Amemiya, Takeshi

• ISBN13: 9780674462250
• ISBN10: 0674462254
• Format: Hardcover
• Copyright: 1994-04-28
• Publisher: Harvard Univ Pr

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

Introduction

What Is Probability?

What Is Statistics?

Probability

Introduction

Axioms of Probability

Counting Techniques

Conditional Probability and Independence

Probability Calculations Exercises

Random Variables And Probability Distributions

Definitions of a Random Variable

Discrete Random Variables

Univariate Continuous Random Variables

Bivariate Continuous Random Variables

Distribution Function

Change of Variables

Joint Distribution of Discrete and Continuous Random Variables Exercises

Moments

Expected Value

Higher Moments

Covariance and Correlation

Conditional Mean and Variance Exercises

Binomial And Normal Random Variables

Binomial Random Variables

Normal Random Variables

Bivariate Normal Random Variables

Multivariate Normal Random Variables Exercises

Large Sample Theory

Modes of Convergence

Laws of Large Numbers and Central Limit Theorems

Normal Approximation of Binomial

Examples Exercises

Point Estimation

What Is an Estimator?

Properties of Estimators

Maximum Likelihood Estimator: Definition and Computation

Maximum Likelihood Estimator: Properties Exercises

Interval Estimation

Introduction

Confidence Intervals

Bayesian Method Exercises

Tests Of Hypotheses

Introduction

Type I and Type II Errors

Neyman-Pearson Lemma

Simple against Composite

Composite against Composite

Examples of Hypothesis Tests

Testing about a Vector Parameter Exercises

Bivariate Regression Model

Introduction

Least Squares Estimators

Tests of Hypotheses Exercises

Elements Of Matrix Analysis

Definition of Basic Terms

Matrix Operations

Determinants and Inverses

Simultaneous Linear Equations

Properties of the Symmetric Matrix Exercises

Multiple Regression Model

Introduction

Least Squares Estimators

Constrained Least Squares Estimators

Tests of Hypotheses

Selection of Regressors Exercises

Econometric Models

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