2021/02/23 by Hurley, Landon
#FOS: Computer and information sciences #Methodology (stat.ME)
paper · doi:10.48550/arxiv.2102.11445
This manuscript develops a general purpose inner-product norm for the Kendall \(τ\) and Spearman's \(ρ\), which operates as an unbiased MLE even in the presence of ties. We derive and prove the strict sub-Gaussianity of the Kemeny norm-space, thereby disproving conclusions developed by both \textcitekendall1948 and \textcitediaconis1977 as to the nature of the appropriate, finite sample, probability distribution and test statistics. A non-parametric MLE framework for all bivariate pairs is developed, thereby resolving an hypothesis of \textciteolkin1994 concerning an exponential multivariate distribution for order statistics, by showing that for finite samples, the distribution is non-exponential. Non-parametric linear estimators are also constructed for the polychoric correlations and by extension, a linearly decomposable non-parametric multidimensional linear system of equations for non-parametric Factor Analysis is shown.