Table of Contents

Statistical Inference

Theory and Calculus of Probability

From Probability to Statistics

Statistical Inference for the Mean based on a Large Sample

Statistical Models and Sampling Distributions

Estimation of Parameters

Confidence Intervals

Hypothesis Testing

Linear Regression

Bayesian Inference

Appendix

About the Author

Jacco Thijssen is a professor of finance at the University of York, UK. Before he joined York, he was at Trinity College Dublin, Ireland, and held visiting positions at LUISS Guido Carli in Rome, Italy, and the Institute of Mathematical Economics at Bielefeld University, Germany. He holds a PhD in mathematical economics from Tilburg University, Netherlands. His main research interests are in the applications of optimal stopping theory, stochastic calculus, and game theory to problems in economics and finance. Professor Thijssen has taught probability theory, statistics, finance, and microeconomics to students of all levels in economics, business, and mathematics. He has received the Aranson Teaching Prize for best organised module twice, as well as a Vice Chancellor’s Teaching Award for his statistics teaching.

Reviews

"The book covers expected topics of any introductory statistics course using simple wording and everyday examples from business, economics, and social sciences. The statistical theory provided for these topics is mathematically and notationally rigorous with minimal steps provided before presenting final results. At the end of each chapter (except Chapter 1), there are exercises and problems for the reader to gain a deeper understanding of the material. Throughout the book, the author references the "two worlds" analogy introduced in Chapter 1, which differentiates between the "real world" and the "sample world." The distinction between these is used in the explanation of various topics to distinguish between what the reader is interested in (theoretically) and what the reader uses (sample information) to form a conclusion. This simple idea, applied many times for different scenarios, is an excellent tool for the reader to get a handle on statistical inference. All-in-all, the book is well conceived, well written, and well executed. Its length and intensity make it best suited as a text for students with strong mathematical backgrounds who have previous exposure to statistics, or as a reference book for those in a mathematical statistics course."
—Analisa M. Flores, University of California, Riverside, in The American Statistician, April 2018"Jacco Thijssen has steered a perfect course in this book, guiding the reader through an overview of statistical analysis that is not only engaging and understandable but also deeper and more substantive than non-technical books on the subject."
—Charles Wheelan teaches public policy at Dartmouth College and is the author of Naked Statistics: Stripping the Dread from the Data"This book is designed to motivate students to learn by making statistics exciting and interesting. I really like the conversational style adopted in conjunction with the emphasis on real world issues both in the text and problem sets. The book concentrates on the basic concepts which encourages understanding and reflection whilst avoiding a superficial "shot gun" approach where many topics do not get the attention they need."
—Brendan McCabe, Management School, University of Liverpool"This is a readable introduction to the principal themes in statistical analysis, aimed primarily at an audience with background in economics, business, finance or social sciences, although science students are also likely to find it useful and enjoyable as a light introductory course. This is thanks to the clear non-patronising style of mathematical exposition combined with thoughtful reflection on the meaning and significance of statistical notions and techniques and on communicating the results of statistical analysis. The book also touches - lightly - on the juxtaposition of the frequentist versus Bayesian philosophical viewpoints. The text very successfully combines a certain simplicity and freshness of style with a degree of sophistication, and challenges the reader to both practice the various statistical techniques and to think critically about them. Numerous examples, problems, and questions make the book useful not only in a classroom setting but also for self-study. I wish I had such a text in my early student days - it would have spared me a lot of frustration sadly inflicted by many other statistics textbooks!"
—Tomasz Zastawniak, Chair of Mathematical Finance, University of York"This book provides a very good introduction to the theory of statistical inference. I am sure that many students will find that it is just what they need….It covers the most important topics in a first course on statistical inference, including: basic probability theory, sampling distributions, estimation, confidence intervals, and hypothesis testing. A final chapter gives a clear introduction to Bayesian methods…The main text is neatly complemented by Exercises and Problems, the latter allowing the reader to use the theory in stylised situations that are similar to problems that can arise in realistic applications… It will work, and work well, for the majority of its intended audience."
—Peter M Lee, Department of Mathematics, University of York, July 2016

"The book covers expected topics of any introductory statistics course using simple wording and everyday examples from business, economics, and social sciences. The statistical theory provided for these topics is mathematically and notationally rigorous with minimal steps provided before presenting final results. At the end of each chapter (except Chapter 1), there are exercises and problems for the reader to gain a deeper understanding of the material. Throughout the book, the author references the "two worlds" analogy introduced in Chapter 1, which differentiates between the "real world" and the "sample world." The distinction between these is used in the explanation of various topics to distinguish between what the reader is interested in (theoretically) and what the reader uses (sample information) to form a conclusion. This simple idea, applied many times for different scenarios, is an excellent tool for the reader to get a handle on statistical inference. All-in-all, the book is well conceived, well written, and well executed. Its length and intensity make it best suited as a text for students with strong mathematical backgrounds who have previous exposure to statistics, or as a reference book for those in a mathematical statistics course."
—Analisa M. Flores, University of California, Riverside, in The American Statistician, April 2018"Jacco Thijssen has steered a perfect course in this book, guiding the reader through an overview of statistical analysis that is not only engaging and understandable but also deeper and more substantive than non-technical books on the subject."
—Charles Wheelan teaches public policy at Dartmouth College and is the author of Naked Statistics: Stripping the Dread from the Data"This book is designed to motivate students to learn by making statistics exciting and interesting. I really like the conversational style adopted in conjunction with the emphasis on real world issues both in the text and problem sets. The book concentrates on the basic concepts which encourages understanding and reflection whilst avoiding a superficial "shot gun" approach where many topics do not get the attention they need."
—Brendan McCabe, Management School, University of Liverpool"This is a readable introduction to the principal themes in statistical analysis, aimed primarily at an audience with background in economics, business, finance or social sciences, although science students are also likely to find it useful and enjoyable as a light introductory course. This is thanks to the clear non-patronising style of mathematical exposition combined with thoughtful reflection on the meaning and significance of statistical notions and techniques and on communicating the results of statistical analysis. The book also touches - lightly - on the juxtaposition of the frequentist versus Bayesian philosophical viewpoints. The text very successfully combines a certain simplicity and freshness of style with a degree of sophistication, and challenges the reader to both practice the various statistical techniques and to think critically about them. Numerous examples, problems, and questions make the book useful not only in a classroom setting but also for self-study. I wish I had such a text in my early student days - it would have spared me a lot of frustration sadly inflicted by many other statistics textbooks!"
—Tomasz Zastawniak, Chair of Mathematical Finance, University of York"This book provides a very good introduction to the theory of statistical inference. I am sure that many students will find that it is just what they need….It covers the most important topics in a first course on statistical inference, including: basic probability theory, sampling distributions, estimation, confidence intervals, and hypothesis testing. A final chapter gives a clear introduction to Bayesian methods…The main text is neatly complemented by Exercises and Problems, the latter allowing the reader to use the theory in stylised situations that are similar to problems that can arise in realistic applications… It will work, and work well, for the majority of its intended audience."
—Peter M Lee, Department of Mathematics, University of York