This book is intended for use in a rigorous introductory PhD level course in econometrics.

A thorough foundation in probability theory and statistical inference provides an introduction to the underlying theory of econometrics that motivates the student at a intuitive as well as a formal level.

The standard introductory texts to mathematical statistics leave the Bayesian approach to be taught later in advanced topics courses-giving students the impression that Bayesian statistics provide but a few techniques appropriate in only special circumstances. Nothing could be further from the truth, argues Dale Poirier, who has developed a course for teaching comparatively both the classical and the Bayesian approaches to econometrics. Poirier's text provides a thoroughly modern, self-contained, comprehensive, and accessible treatment of the probability and statistical foundations of econometrics with special emphasis on the linear regression model. Written primarily for advanced undergraduate and graduate students who are pursuing research careers in economics, Intermediate Statistics and Econometrics offers a broad perspective, bringing together a great deal of diverse material. Its comparative approach, emphasis on regression and prediction, and numerous exercises and references provide a solid foundation for subsequent courses in econometrics and will prove a valuable resource to many nonspecialists who want to update their quantitative skills. The introduction closes with an example of a real-world data set-the Challengerspace shuttle disaster-that motivates much of the text's theoretical discussion. The ten chapters that follow cover basic concepts, special distributions, distributions of functions of random variables, sampling theory, estimation, hypothesis testing, prediction, and the linear regression model. Appendixes contain a review of matrix algebra, computation, and statistical tables.

Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.

This empirical research methods course enables informed implementation of statistical procedures, giving rise to trustworthy evidence.

Mathematical Statistics for Economics and Business, Second Edition, provides a comprehensive introduction to the principles of mathematical statistics which underpin statistical analyses in the fields of economics, business, and econometrics. The selection of topics in this textbook is designed to provide students with a conceptual foundation that will facilitate a substantial understanding of statistical applications in these subjects. This new edition has been updated throughout and now also includes a downloadable Student Answer Manual containing detailed solutions to half of the over 300 end-of-chapter problems. After introducing the concepts of probability, random variables, and probability density functions, the author develops the key concepts of mathematical statistics, most notably: expectation, sampling, asymptotics, and the main families of distributions. The latter half of the book is then devoted to the theories of estimation and hypothesis testing with associated examples and problems that indicate their wide applicability in economics and business. Features of the new edition include: a reorganization of topic flow and presentation to facilitate reading and understanding; inclusion of additional topics of relevance to statistics and econometric applications; a more streamlined and simple-to-understand notation for multiple integration and multiple summation over general sets or vector arguments; updated examples; new end-of-chapter problems; a solution manual for students; a comprehensive answer manual for instructors; and a theorem and definition map. This book has evolved from numerous graduate courses in mathematical statistics and econometrics taught by the author, and will be ideal for students beginning graduate study as well as for advanced undergraduates.