Probability, statistics and econometrics / Oliver Linton.

Format:

Book

Author/Creator:

Linton, Oliver, author.

Language:

English

Subjects (All):

Mathematical statistics.

Physical Description:

1 online resource (390 pages) : illustrations (some color)

Edition:

1st ed.

Place of Publication:

London, England : Academic Press, 2017.

Summary:

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. -- Provided by publisher.

Contents:

Front Cover

Probability, Statistics and Econometrics

Copyright

Contents

List of Figures

About the Author

Preface

Acknowledgment

Part I Probability and Distribution

1 Probability Theory

1.1 Introduction

1.2 De nition of Probability

1.3 Some Counting Problems

2 Conditional Probability and Independence

2.1 Conditional Probability

2.2 Bayes Theorem

2.3 Independence

3 Random Variables, Distribution Functions, and Densities

3.1 Random Variables

3.2 Distribution Functions

3.3 Quantile

3.4 Density and Mass Functions

4 Transformations of Random Variables

4.1 Distributions of Functions of a Random Variable

4.2 Probability Integral Transform

5 The Expectation

5.1 De nition and Properties

5.2 Additional Moments and Cumulants

5.3 An Interpretation of Expectation and Median

6 Examples of Univariate Distributions

6.1 Parametric Families of Distributions

7 Multivariate Random Variables

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

8 Asymptotic Theory

8.1 Inequalities

8.2 Notions of Convergence

8.3 Laws of Large Numbers and CLT

8.4 Some Additional Tools

9 Exercises and Complements

Part II Statistics

10 Introduction

10.1 Sampling Theory

10.2 Sample Statistics

10.3 Statistical Principles

11 Estimation Theory

11.1 Estimation Methods

11.2 Comparison of Estimators and Optimality

11.3 Robustness and Other Issues with the MLE

12 Hypothesis Testing

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

13 Con dence Intervals and Sets

13.1 De nitions.

13.2 Likelihood Ratio Con dence Interval

13.3 Methods of Evaluating Intervals

14 Asymptotic Tests and the Bootstrap

14.1 Simulation Methods

14.2 Bootstrap

15 Exercises and Complements

Part III Econometrics

16 Linear Algebra

16.1 Matrices

16.2 Systems of Linear Equations and Projection

17 The Least Squares Procedure

17.1 Projection Approach

17.2 Partitioned Regression

17.3 Restricted Least Squares

18 Linear Model

18.1 Introduction

18.2 The Model

19 Statistical Properties of the OLS Estimator

19.1 Properties of OLS

19.2 Optimality

20 Hypothesis Testing for Linear Regression

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

21 Omission of Relevant Variables, Inclusion of Irrelevant Variables, and Model Selection

21.1 Omission of Relevant Variables

21.2 Inclusion of Irrelevant Variables/Knowledge of Parameters

21.3 Model Selection

21.4 Lasso

22 Asymptotic Properties of OLS Estimator and Test Statistics

22.1 The I.I.D. Case

22.2 The Non-I.I.D. Case

23 Generalized Method of Moments and Extremum Estimators

23.1 Generalized Method Moments

23.2 Asymptotic Properties of Extremum Estimators

23.3 Quantile Regression

24 A Nonparametric Postscript

25 A Case Study

26 Exercises and Complements

Appendix

A Some Results from Calculus

B Some Matrix Facts

B.1 Matrix Operations Satisfy Certain Mathematical Laws

B.2 Transpose of a Matrix

B.3 Inverse

B.4 Trace of a Matrix

B.5 Determinant of a Matrix

B.6 Rank of a Matrix

B.7 Eigenvalues of Real Symmetric Matrix

B.8 Positive De niteness

Bibliography

Index

Back Cover.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-12-810496-1