Galton used quantiles more than a hundred years ago in describing data. Tukey and Parzen used them in the 60s and 70s in describing populations. Since then, the authors of many papers, both theoretical and practical, have used various aspects of quantiles in their work. Until now, however, no one put all the ideas together to form what turns out to
Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.
Originally published in 1986, this valuable reference provides a detailed treatment of limit theorems and inequalities for empirical processes of real-valued random variables; applications of the theory to censored data, spacings, rank statistics, quantiles, and many functionals of empirical processes, including a treatment of bootstrap methods; and a summary of inequalities that are useful for proving limit theorems. At the end of the Errata section, the authors have supplied references to solutions for 11 of the 19 Open Questions provided in the book's original edition. Audience: researchers in statistical theory, probability theory, biostatistics, econometrics, and computer science.
This book provides a fresh approach to reliability theory, an area that has gained increasing relevance in fields from statistics and engineering to demography and insurance. Its innovative use of quantile functions gives an analysis of lifetime data that is generally simpler, more robust, and more accurate than the traditional methods, and opens the door for further research in a wide variety of fields involving statistical analysis. In addition, the book can be used to good effect in the classroom as a text for advanced undergraduate and graduate courses in Reliability and Statistics.
Collection of papers presented at the Colloquium, covering the broad subject areas of spatial data integration, statistical analysis of geoscience data, and quantitative stratigraphy. Working Group reports are included as well.
This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concern ing the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense. Contrary to the classical limit theorems that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approxi mating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. Other recent developments in statistics like nonparametric curve estima tion and the bootstrap method will be studied as far as order statistics are concerned. 1n connection with this, graphical methods will, to some extent, be explored.
Since the contributions to this volume stem from very different fields, no attempt was made to find a systematic ordering. All results are new in so far as they have not been published so far.
A guide to the implementation and interpretation of Quantile Regression models This book explores the theory and numerous applications of quantile regression, offering empirical data analysis as well as the software tools to implement the methods. The main focus of this book is to provide the reader with a comprehensive description of the main issues concerning quantile regression; these include basic modeling, geometrical interpretation, estimation and inference for quantile regression, as well as issues on validity of the model, diagnostic tools. Each methodological aspect is explored and followed by applications using real data. Quantile Regression: Presents a complete treatment of quantile regression methods, including, estimation, inference issues and application of methods. Delivers a balance between methodolgy and application Offers an overview of the recent developments in the quantile regression framework and why to use quantile regression in a variety of areas such as economics, finance and computing. Features a supporting website (www.wiley.com/go/quantile_regression) hosting datasets along with R, Stata and SAS software code. Researchers and PhD students in the field of statistics, economics, econometrics, social and environmental science and chemistry will benefit from this book.