An Introductory Econometrics Text
Mathematical Statistics for Applied Econometrics covers the basics of statistical inference in support of a subsequent course on classical econometrics. The book shows students how mathematical statistics concepts form the basis of econometric formulations. It also helps them think about statistics as more than a toolbox of techniques.
Uses Computer Systems to Simplify Computation
The text explores the unifying themes involved in quantifying sample information to make inferences. After developing the necessary probability theory, it presents the concepts of estimation, such as convergence, point estimators, confidence intervals, and hypothesis tests. The text then shifts from a general development of mathematical statistics to focus on applications particularly popular in economics. It delves into matrix analysis, linear models, and nonlinear econometric techniques.
Students Understand the Reasons for the Results
Avoiding a cookbook approach to econometrics, this textbook develops students’ theoretical understanding of statistical tools and econometric applications. It provides them with the foundation for further econometric studies.
DEFINING RANDOM VARIABLES
Introduction to Statistics, Probability and Econometrics
Relating Mathematical Statistics and Economics
Basics of Probability
Random Variables and Probability Distributions
Uniform Probability Measure
Random Variables and Distributions
Basic Concept of Random Variables
Univariate Continuous Random Variables
Some Common Univariate Distribution Functions
Multivariate Random Variables
Change of Variables
Derivation of the Normal Distribution Function
An Applied Sabbatical
Moments and Moment Generating Functions
Expected Values
Moments
Covariance and Correlation
Conditional Mean and Variance
Moment Generating Functions
Binomial and Normal Random Variables
Bernoulli Random Variables
Binomial Random Variables
Univariate Normal Distribution
Linking the Normal Distribution to the Binomial
Bivariate and Multivariate Normal Random Variables
ESTIMATION
Large Sample Theory
Basic Sample Theory
Modes of Convergence
Laws of Large Numbers
Asymptotic Normality
Characteristic Functions
Wrapping Up Loose Ends
Point Estimation
What Is an Estimator?
Mean Squared Error
Sufficient Statistics
Concentrated Likelihood Functions
Normal Equations
Properties of Maximum Likelihood Estimators
Interval Estimation
Confidence Intervals
Bayesian Estimation
Bayesian Confidence Intervals
Testing Hypothesis
Type I and Type II Errors
Neyman-Pearson Lemma
Simple Tests against a Composite
Composite against a Composite
Testing Hypothesis about Vectors
ECONOMETRIC APPLICATIONS
Elements of Matrix Analysis
Review of Elementary Matrix Algebra
Projection Matrices
Idempotent Matrices
Eigenvalues and Eigenvectors
Kronecker Products
Regression Applications in Econometrics
Simple Linear Regression
Multivariate Regression
Linear Restrictions
Exceptions to Ordinary Least Squares
Notes
Bibliography
Index
Biography
Charles B Moss
"Its goals are to cover the basics of statistical inference in support of a subsequent econometrics course and to explain the ’why’ to motivate the students who had previously taken an introductory statistics or econometrics course of a cookbook flavour. Such a textbook is needed, as several popular econometrics textbooks put fundamentals of mathematical statistics in an appendix … [T]he book shows how mathematical statistics is useful in econometrics and economic decisions under uncertainty and risk. It carefully explains the logic underlying estimators and tests, with an emphasis on laying a solid foundation for their uses in the subsequent applications. It is very useful to introduce and use the symbolic programs Maxima and MathematicaTM for the mathematical calculations, in addition to the open source package R for the numerical and graphical tasks. The textbook also has web resources with lecture slides, data sets and computer programs … and can be used both by graduate students from economics, business and various other backgrounds and by instructors and practitioners as a reference."
—Shuangzhe Liu in Stastistical Papers, October 2016"This book presents a useful and well-integrated connection between mathematical statistics and applied econometrics. There is a natural progression from probability theory to estimations to economics applications, and the examples are helpful to understand and illustrate the statistical concepts. I highly recommend it to students who want to understand statistical theory that is driving econometrics applications frequently used in economics research."
—Ani Katchova, Associate Professor, Agricultural Economics, University of Kentucky"This book is a formal yet accessible introductory textbook to mathematical statistics, with a clear emphasis on building a strong background for the subsequent study of econometric methods employed in social sciences, agricultural economics, finance, and agribusiness. The book’s intended audiences are graduate students—very strong masters and all doctoral students—and professionals looking for an intuitive and easy-to use reference. The text is ideal for a one-semester or one-year course in mathematical statistics.
The book is a pleasure to read: it offers great perspectives through the use of ‘boxes’ that provide historical context and interesting facts. They represent a fun companion in the journey of learning the formal concepts of mathematical statistics throughout the book. In addition, the examples and applications are useful and intuitive, having in mind students in economics, agricultural economics, and business. The end-of-chapter exercises are adequate and do not go overboard."
—Alfonso Flores-Lagunes, Professor of Economics and Senior Research Associate, Center for Policy Research, Syracuse University, and Research Fellow, Institute for the Study of Labor (IZA)
