1st Edition
Introduction to the Theory of Statistical Inference
Based on the authors’ lecture notes, Introduction to the Theory of Statistical Inference presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Suitable for a second-semester undergraduate course on statistical inference, the book offers proofs to support the mathematics. It illustrates core concepts using cartoons and provides solutions to all examples and problems.
Highlights
- Basic notations and ideas of statistical inference are explained in a mathematically rigorous, but understandable, form
- Classroom-tested and designed for students of mathematical statistics
- Examples, applications of the general theory to special cases, exercises, and figures provide a deeper insight into the material
- Solutions provided for problems formulated at the end of each chapter
- Combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models
- Theoretical, difficult, or frequently misunderstood problems are marked
The book is aimed at advanced undergraduate students, graduate students in mathematics and statistics, and theoretically-interested students from other disciplines. Results are presented as theorems and corollaries. All theorems are proven and important statements are formulated as guidelines in prose. With its multipronged and student-tested approach, this book is an excellent introduction to the theory of statistical inference.
Introduction
Statistical model
Data
Statistical Model
Statistic
Exponential Families
List of Problems
Further Reading
Inference Principles
Likelihood Function
Fisher Information
Sufficiency
List of Problems
Further Reading
Estimation
Methods of Estimation
Unbiasedness and Mean Squared Error
Asymptotic Properties of Estimators
List of Problems
Further Reading
Testing Hypotheses
Test problems
Tests: Assessing Evidence
Tests: Decision Rules
List of Problems
Further Reading
Linear Model
Introduction
Formulation of the Model
The Least Squares Estimator
The Normal Linear Model
List of Problems
Further Reading
Solutions
Bibliography
Index
Biography
Hannelore Liero is an apl. Prof. for Mathematical Statistics at the University of Potsdam. She studied Mathematics at the Humboldt-University in Berlin. She earned her Ph.D. while working as a scientist at the Academy of Sciences of the GDR. Since 1992, she has taught Statistics for undergraduate and graduate students in Mathematics, Biology and Computer Science at the Faculty of Sciences at the University of Potsdam. In addition to teaching, she does basic research in Statistics and supports scientists applying statistical methods in practice. Silvelyn Zwanzig is an Associate Professor for Mathematical Statistics at Uppsala University. She studied Mathematics at the Humboldt-University in Berlin. Before coming to Sweden she was Assistant Professor at the University of Hamburg in Germany. She received her Ph.D. in Mathematics at the Academy of Sciences of the GDR. Since 1991, she has taught Statistics for undergraduate and graduate students. Her research interests have moved from theoretical statistics to computer intensive statistics. She is interested in consulting and was working in Astrometry.
… it provides in-depth explanations, complete with proofs, of how statistics works. … The book has several user-friendly aspects. One is the use of eight example data sets to illustrate the theory throughout the text. This repeated use of the same examples allows readers to focus their energy on applying a theoretical point under discussion to a familiar example rather than having to first become acquainted with a new example. Another big help are the detailed solutions provided for the problems that appear at the end of each chapter. … Also helpful: Theoretical or difficult material that can be skipped is marked with an asterisk. … a clear exposition of the theory of statistical inference, along with complete proofs and familiar examples. The text analyzes not just methods one learns in a first statistics course, but alternatives as well. Each chapter is capped by a further reading section that is at once comprehensive and concise.
—David A. Huckaby, MAA Reviews, February 2012
