Statistical methods for ranking data
This book presents a compilation of the authors' research on various ranking methods, with a focus on real applications. The main objective is to illustrate the statistical analysis of ranking data. Ranking data is equivalent to finding the order of preference with respect to a set of objects. Given \(t\) objects labelled by integers 1 to \(t\), a ranking is a given permutation of the integers \((1, 2, \ldots, t)\), denoted as \(\mu = (\mu(1), \mu(2), \ldots, \mu(t))'\). The monograph first introduces notions on visualisation of ranking data and on correlation between rankings. Two chapters follow that present tests for randomness in complete and incomplete block designs. Then, a general theory of hypothesis testing is developed. The second part of the book deals with probability and statistical modelling for ranking data. Multivariate normal order statistics models, factor analysis, decision tree models, and extensions of distance-based models are introduced. Finally, the appendices provide access to real ranking data sets as well as extra material on limit theorems and decision trees. The book is written at the level of a research monograph and is best suited for senior undergraduate and graduate students. The procedures are often illustrated by applications to real data sets. R code and further data sets can be accessed in a companion web site to the book (\url{http://web.hku.hk/~plhyu/StatMethRank/}), therefore, the volume can very well serve as a textbook for courses on statistical methods for ranking data.
scientific article; zbMATH DE number 6349262