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
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