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This book introduces advanced undergraduate, graduate students and practitioners to statistical methods for ranking data. An important aspect of nonparametric statistics is oriented towards the use of ranking data. Rank correlation is defined through the notion of distance functions and the notion of compatibility is introduced to deal with incomplete data. Ranking data are also modeled using a variety of modern tools such as CART, MCMC, EM algorithm and factor analysis. This book deals with statistical methods used for analyzing such data and provides a novel and unifying approach for hypotheses testing. The techniques described in the book are illustrated with examples and the statistical software is provided on the authors’ website.
This book is the first single source volume to fully address this prevalent practice in both its analytical and modeling aspects. The information discussed presents the use of data consisting of rankings in such diverse fields as psychology, animal science, educational testing, sociology, economics, and biology. This book systematically presents th
In June of 1990, a conference was held on Probablity Models and Statisti cal Analyses for Ranking Data, under the joint auspices of the American Mathematical Society, the Institute for Mathematical Statistics, and the Society of Industrial and Applied Mathematicians. The conference took place at the University of Massachusetts, Amherst, and was attended by 36 participants, including statisticians, mathematicians, psychologists and sociologists from the United States, Canada, Israel, Italy, and The Nether lands. There were 18 presentations on a wide variety of topics involving ranking data. This volume is a collection of 14 of these presentations, as well as 5 miscellaneous papers that were contributed by conference participants. We would like to thank Carole Kohanski, summer program coordinator for the American Mathematical Society, for her assistance in arranging the conference; M. Steigerwald for preparing the manuscripts for publication; Martin Gilchrist at Springer-Verlag for editorial advice; and Persi Diaconis for contributing the Foreword. Special thanks go to the anonymous referees for their careful readings and constructive comments. Finally, we thank the National Science Foundation for their sponsorship of the AMS-IMS-SIAM Joint Summer Programs. Contents Preface vii Conference Participants xiii Foreword xvii 1 Ranking Models with Item Covariates 1 D. E. Critchlow and M. A. Fligner 1. 1 Introduction. . . . . . . . . . . . . . . 1 1. 2 Basic Ranking Models and Their Parameters 2 1. 3 Ranking Models with Covariates 8 1. 4 Estimation 9 1. 5 Example. 11 1. 6 Discussion. 14 1. 7 Appendix . 15 1. 8 References.
Volume III includes more selections of articles that have initiated fundamental changes in statistical methodology. It contains articles published before 1980 that were overlooked in the previous two volumes plus articles from the 1980's - all of them chosen after consulting many of today's leading statisticians.
Data on water quality and other environmental issues are being collected at an ever-increasing rate. In the past, however, the techniques used by scientists to interpret this data have not progressed as quickly. This is a book of modern statistical methods for analysis of practical problems in water quality and water resources.The last fifteen years have seen major advances in the fields of exploratory data analysis (EDA) and robust statistical methods. The 'real-life' characteristics of environmental data tend to drive analysis towards the use of these methods. These advances are presented in a practical and relevant format. Alternate methods are compared, highlighting the strengths and weaknesses of each as applied to environmental data. Techniques for trend analysis and dealing with water below the detection limit are topics covered, which are of great interest to consultants in water-quality and hydrology, scientists in state, provincial and federal water resources, and geological survey agencies.The practising water resources scientist will find the worked examples using actual field data from case studies of environmental problems, of real value. Exercises at the end of each chapter enable the mechanics of the methodological process to be fully understood, with data sets included on diskette for easy use. The result is a book that is both up-to-date and immediately relevant to ongoing work in the environmental and water sciences.
A coherent, unified set of statistical methods, based on ranks, for analyzing data resulting from various experimental designs. Uses MINITAB, a statistical computing system for the implementation of the methods. Assesses the statistical and stability properties of the methods through asymptotic efficiency and influence curves and tolerance values. Includes exercises and problems.
The mathematics behind today's most widely used rating and ranking methods A website's ranking on Google can spell the difference between success and failure for a new business. NCAA football ratings determine which schools get to play for the big money in postseason bowl games. Product ratings influence everything from the clothes we wear to the movies we select on Netflix. Ratings and rankings are everywhere, but how exactly do they work? Who's #1? offers an engaging and accessible account of how scientific rating and ranking methods are created and applied to a variety of uses. Amy Langville and Carl Meyer provide the first comprehensive overview of the mathematical algorithms and methods used to rate and rank sports teams, political candidates, products, Web pages, and more. In a series of interesting asides, Langville and Meyer provide fascinating insights into the ingenious contributions of many of the field's pioneers. They survey and compare the different methods employed today, showing why their strengths and weaknesses depend on the underlying goal, and explaining why and when a given method should be considered. Langville and Meyer also describe what can and can't be expected from the most widely used systems. The science of rating and ranking touches virtually every facet of our lives, and now you don't need to be an expert to understand how it really works. Who's #1? is the definitive introduction to the subject. It features easy-to-understand examples and interesting trivia and historical facts, and much of the required mathematics is included.
Few books on statistical data analysis in the natural sciences are written at a level that a non-statistician will easily understand. This is a book written in colloquial language, avoiding mathematical formulae as much as possible, trying to explain statistical methods using examples and graphics instead. To use the book efficiently, readers should have some computer experience. The book starts with the simplest of statistical concepts and carries readers forward to a deeper and more extensive understanding of the use of statistics in environmental sciences. The book concerns the application of statistical and other computer methods to the management, analysis and display of spatial data. These data are characterised by including locations (geographic coordinates), which leads to the necessity of using maps to display the data and the results of the statistical methods. Although the book uses examples from applied geochemistry, and a large geochemical survey in particular, the principles and ideas equally well apply to other natural sciences, e.g., environmental sciences, pedology, hydrology, geography, forestry, ecology, and health sciences/epidemiology. The book is unique because it supplies direct access to software solutions (based on R, the Open Source version of the S-language for statistics) for applied environmental statistics. For all graphics and tables presented in the book, the R-scripts are provided in the form of executable R-scripts. In addition, a graphical user interface for R, called DAS+R, was developed for convenient, fast and interactive data analysis. Statistical Data Analysis Explained: Applied Environmental Statistics with R provides, on an accompanying website, the software to undertake all the procedures discussed, and the data employed for their description in the book.
Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications. The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.
Statistics is a pillar of machine learning. You cannot develop a deep understanding and application of machine learning without it. Cut through the equations, Greek letters, and confusion, and discover the topics in statistics that you need to know. Using clear explanations, standard Python libraries, and step-by-step tutorial lessons, you will discover the importance of statistical methods to machine learning, summary stats, hypothesis testing, nonparametric stats, resampling methods, and much more.