Third Special Issue On Statistical Data Analysis Based On The L1 Norm And Related Methods

Statistical Data Analysis Based on the L1-Norm and Related Methods

This volume contains a selection of invited papers, presented to the fourth In Statistical Analysis Based on the L1-Norm and Related ternational Conference on Methods, held in Neuchatel, Switzerland, from August 4-9, 2002. Organized jointly by the University of Illinois at Chicago (Gib Bassett), the Rutgers University (Regina Liu and Yehuda Vardi) and the University of Neuchatel (Yadolah Dodge), the conference brought together experts whose research deals with theory and ap plications involving the L1-Norm. The conference included invited and contributed talks as well as a tutorial on Quantile Regression. This volume includes 36 refereed invited papers under seven headings. Part one deals with Quantiles in all their forms and shapes. It includes papers on quantile functions in non-parametric multivariate analysis, and empirical applications of quantile regression. Much of the development in this direction follows from the fundamental paper by Koenker and Bassett in 1978. Financial and Time Series A nalysis follows the section on quantiles. Part three concerns Estimation, Testing and Characterization. Part four, Deep in the Data, deals with issues related to data depth. Part five addresses Classification questions. The problem of Density Estimation and Image Processing is discussed in Part six, and finally Part seven presents two environmental applications. The contributions represent clear evidence of important research involving theo retical issues and applications associated with the L1-Norm. It is my hope that the articles contained in this volume and its predecessors, published in 1987, 1992, and 1997, will stimulate interest among researchers.

Third Special Issue on Statistical Data Analysis Based on the L1 Norm and Related Methods

Linear Models and Generalizations

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.