Parameters behind “Nonparametric” Statistics: Kendall's tau, Somers’ D and Median Differences

Confidence intervals for rank statistics: Somers’ D and extensions

Somers’ D is an asymmetric measure of association between two variables, which plays a central role as a parameter behind rank or “non–parametric” statistical methods. Given a predictor variable X and an outcome variable Y , we may estimate DY X as a measure of the effect of X on Y , or we may estimate DXY as a performance indicator of X as a predictor of Y . The somersd package allows the esti...

Nonparametric Statistics

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Interpretation of Somers’ D under four simple models

(where E[·] denotes expectation), or, equivalently, as the difference between the probability that the two X,Y –pairs are concordant and the probability that the two X,Y –pairs are discordant. A pair of X,Y –pairs is said to be concordant if the larger X–value is paired with the larger Y –value, and is said to be discordant if the larger X–value is paired with the smaller Y –value. Somers’ D of...

Nonparametric statistics on manifolds

This article presents certain recent methodologies and some new results for the statistical analysis of probability distributions on manifolds. An important example considered in some detail here is the 2-D shape space of k-ads, comprising all configurations of k planar landmarks (k > 2)-modulo translation, scaling and rotation.

Nonparametric Statistics, ENAR