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, as well as 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
