Linear Model Theory: With Examples and Exercises

This textbook provides a comprehensive and rigorous approach to best linear unbiased estimation and prediction in linear models, with illustrations and exercises. It is intended for master and PhD students and instructors of linear models courses.

Format: Paperback / softback
Length: 504 pages
Publication date: 03 November 2021
Publisher: Springer Nature Switzerland AG

This comprehensive textbook offers a unified and rigorous framework for best linear unbiased estimation and prediction of parameters and random quantities in linear models, as well as other theoretical foundations upon which much of the statistical methodology associated with these models is built. One of the book's most distinctive features is its ability to illustrate each major concept or result with one or more concrete examples or special cases, making it highly accessible and engaging for students. Throughout the text, commonly used methodologies based on the theory are presented in methodological interludes, accompanied by a wealth of exercises that will greatly benefit both students and instructors.

To facilitate computations, generalized inverses are employed throughout, allowing the model matrix and other matrices to have non-full rank. Greater emphasis is placed on estimability, partitioned analyses of variance, constrained least squares, the effects of model misspecification, and, particularly, prediction compared to many other textbooks on linear models. This book is designed for advanced master's and PhD students with a solid foundation in statistical theory, matrix algebra, and applied regression analysis. Additionally, it serves as a valuable resource for instructors teaching courses on linear models. Solutions to the book's exercises are available in the companion volume Linear Model Theory - Exercises and Solutions, authored by the same author.

Weight: 801g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030520656
Edition number: 1st ed. 2020