A pioneering monograph on tensor methods applied to distributional problems arising in statistics, this work constitutes a valuable reference for graduate students and professional statisticians. Prerequisites include some knowledge of linear algebra, eigenvalue decompositions, and linear models as well as likelihood functions and likelihood ratio statistics. Index notation is the favored mode of expression throughout the book. The first chapter introduces a number of aspects of index notation, groups, invariants, and tensor calculus, with examples drawn from linear algebra, physics, and statistics. Subsequent chapters form the core of the text, addressing moments, cumulants, and invariants. Additional topics include sample cumulants, Edgeworth series, saddlepoint approximation, likelihood functions, and ancillary statistics. More than 200 exercises form an integral part of the text.
About the Author
Peter McCullagh studied at The University of Birmingham and received his Ph.D. from Imperial College, London. He is the John D. MacArthur Distinguished Service Professor in the Department of Statistics and the College at The University of Chicago. He is also the co-author (with John Nelder) of Generalized Linear Models (Chapman and Hall, 1983, second edition 1989) which received the inaugural Karl Pearson Prize from the International Statistics Institute. He is a member of The Royal Society (UK) and The American Academy of Arts and Sciences.