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Linear Models and Generalizations

Least Squares and Alternatives

C. Radhakrishna Rao, Helge Toutenburg, Shalabh, Christian Heumann (Autoren)

Buch | Hardcover

XIX, 572 Seiten

2007 | 3rd, extended ed. 2008
Springer Berlin (Verlag)
978-3-540-74226-5 (ISBN)

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Thebookisbasedonseveralyearsofexperienceofbothauthorsinteaching linear models at various levels. It gives an up-to-date account of the theory and applications of linear models. The book can be used as a text for courses in statistics at the graduate level and as an accompanying text for courses in other areas. Some of the highlights in this book are as follows. A relatively extensive chapter on matrix theory (Appendix A) provides the necessary tools for proving theorems discussed in the text and o?ers a selectionofclassicalandmodernalgebraicresultsthatareusefulinresearch work in econometrics, engineering, and optimization theory. The matrix theory of the last ten years has produced a series of fundamental results aboutthe de?niteness ofmatrices,especially forthe di?erences ofmatrices, which enable superiority comparisons of two biased estimates to be made for the ?rst time. We have attempted to provide a uni?ed theory of inference from linear models with minimal assumptions. Besides the usual least-squares theory, alternative methods of estimation and testing based on convex loss fu- tions and general estimating equations are discussed. Special emphasis is given to sensitivity analysis and model selection. A special chapter is devoted to the analysis of categorical data based on logit, loglinear, and logistic regression models. The material covered, theoretical discussion, and a variety of practical applications will be useful not only to students but also to researchers and consultants in statistics.

Helge Toutenburg studierte (1961-1966) und promovierte (1969) in Berlin, habilitierte in Dortmund (1989). Er ist seit 1991 Professor für Statistik an der Ludwig-Maximilians-Universität München.

The Simple Linear Regression Model.- The Multiple Linear Regression Model and Its Extensions.- The Generalized Linear Regression Model.- Exact and Stochastic Linear Restrictions.- Prediction in the Generalized Regression Model.- Sensitivity Analysis.- Analysis of Incomplete Data Sets.- Robust Regression.- Models for Categorical Response Variables.

From the reviews of the third edition:

"The book contains a massive amount of useful results related to the world of linear models. ... I find my life more comfortable when I have this book in my bookshelf while checking whether some results have appeared in the literature. ... a natural source book for a student and researcher of linear models. ... written with great care and, of course, with great skills under the leadership of Professor C. Radhakrishna Rao. This is a very useful book and the authors earn congratulations." (Simo Puntanen, International Statistical Review, Vol. 75 (3), 2007)

"The book gives an up-to-date and comprehensive account of the theory and applications of linear models along with a number of new results. Throughout its ten chapters as well as its appendices, it covers theoretical issues and practical applications that make it suitable and useful not only to students but also to researchers and consultants in statistics." (Vangelis Grigoroudis, Zentralblatt MATH, Vol. 1151, 2009)

"This book has two laudable strengths. First, the coverage of topics is vast and varied. Second, extensive material is included on many modern, cutting-edge directions. ... The book would also function as an excellent reference for graduate students and researchers on classical and current developments in linear model theory." (Joseph Cavanaugh, Journal of the American Statistical Association, Vol. 104 (486), June, 2009)

Erscheint lt. Verlag	12.10.2007
Reihe/Serie	Springer Series in Statistics
Co-Autor	M. Schomaker
Zusatzinfo	XIX, 572 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1010 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	best fit • Calculus • Econometrics • Fitting • Generalized Linear Model • Least Squares • likelihood • linear regression • Optimization • optimization theory • Regression • Regression (Statistik) • Statistics
ISBN-10	3-540-74226-3 / 3540742263
ISBN-13	978-3-540-74226-5 / 9783540742265
Zustand	Neuware