Linear Models and Generalizations

Least Squares and Alternatives

  • C. Radhakrishna Rao
  • Shalabh 
  • Helge Toutenburg
  • Christian Heumann

Part of the Springer Series in Statistics book series (SSS)

About this book

Introduction

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.

Keywords

Fitting Generalized linear model Least Squares Likelihood Optimization Theory Regression best fit calculus econometrics linear regression optimization statistics

Authors and affiliations

  • C. Radhakrishna Rao
    • 1
  • Shalabh 
    • 2
  • Helge Toutenburg
    • 3
  • Christian Heumann
    • 3
  1. 1.Department of StatisticsPennsylvania State UniversityUniversity ParkUSA
  2. 2.Department of Mathematics & StatisticsIndian Institute of TechnologyKanpurIndia
  3. 3.Institut für StatistikLudwig-Maximilians-UniversitätMünchenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-74227-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-74226-5
  • Online ISBN 978-3-540-74227-2
  • Series Print ISSN 0172-7397
  • About this book