Mathematical Sciences: Methods for Ranked Data

点击翻译按钮获取中文摘要

In ranked data each observation is a permutation of n items. Because the permutations do not have a natural linear ordering, many common statistical methods are inappropriate for ranked data. However, the permutations of n items can be naturally placed on the vertices of a polytope inscribed in a sphere in n-1 dimensional Euclidean space. This geometry suggests new graphical and analytical methods for analyzing full and partially ranked data. Of particular interest are probability density histograms, spectral analysis, kernal smoothing methods, and confidence regions. Statistical methods are proposed to analyze ranked data. Ranked data occur when a group of "judges" are asked to evaluate a set of items and then to rank them in order of preference. Hence, each "judge" states his first, second, etc., and last choices among the items that he has evaluated. Proper methods to graphically display and analyze ranked data are very important. This type of data is encountered frequently in the social sciences, in market research, and in elections. A less well known, but equally important area in which ranked data are encountered is expert systems for military applications.