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.
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.
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.
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