Statistical Methods for Ranking Data

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.

Introduction.- Exploratory Analysis of Ranking Data.- Correlation Analysis of Paired Ranking Data.- Testing for randomness, agreement and interaction.- Block Designs.- General Theory of Hypothesis Testing.- Testing for Ordered Alternatives.- Probability Models for Ranking Data.- Probit Models for Ranking Data.- Decision Tree Models for Ranking Data.- Extension of Distance-Based Models for Ranking Data.- Appendix A: Ranking Data Sets.- Appendix B: Limit Theorems.- Appendix C: Review on Decision Trees.