Geometry of rank tests
نویسندگان
چکیده
We study partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equivalence classes. These permutations are the linear extensions of partially ordered sets specified by the data. Our methods refine rank tests of non-parametric statistics, such as the sign test and the runs test, and are useful for the exploratory analysis of ordinal data. Convex rank tests correspond to probabilistic conditional independence structures known as semi-graphoids. Submodular rank tests are classified by the faces of the cone of submodular functions, or by Minkowski summands of the permutohedron. We enumerate all small instances of such rank tests. Graphical tests correspond to both graphical models and to graph associahedra, and they have excellent statistical and algorithmic properties.
منابع مشابه
Triple factorization of non-abelian groups by two maximal subgroups
The triple factorization of a group $G$ has been studied recently showing that $G=ABA$ for some proper subgroups $A$ and $B$ of $G$, the definition of rank-two geometry and rank-two coset geometry which is closely related to the triple factorization was defined and calculated for abelian groups. In this paper we study two infinite classes of non-abelian finite groups $D_{2n}$ and $PSL(2,2^{n})$...
متن کاملExplicit tensors of border rank at least 2n-1
For odd m, I write down tensors in C m ⊗C m ⊗C m of border rank at least 2m − 1, showing the non-triviality of the Young-flattening equations of [6] that vanish on the matrix multiplication tensor. I also study the border rank of the tensors of [1] and [3]. I show the tensors T 2 k ∈ C k ⊗C 2 k ⊗C 2 k , of [1], despite having rank equal to 2 k+1 − 1, have border rank equal to 2 k. I show the eq...
متن کاملInvestigation of Pedological criterion Affecting on Desertification in Alluvial Fans Using Nonparametric Tests, Case Study: South of Rude-Shoor Watershed Area
Investigation of desertification trend needs an understanding phenomena creating changes singly or action and reaction together in the manner that these changes end up in land degradation and desertification. In the investigation of pedological criterion affecting on land degradation in alluvial fans, first, maps of slope classes, land use and geology were created, then a map of units was found...
متن کاملIntroduction : The geometry of data
In multivariate analysis, data often cannot be fitted by normal or, more general, elliptically symmetric distributions. Then the classical parametric methodology, which draws on normality or ellipticity, fails. Recently, non-parametric methods have been developed that exploit the geometrical structure of the data in an explicit way and make use of the analyst's geometric intuition. They include...
متن کاملObservability of Linear Hybrid Systems
We analyze the observability of the continuous and discrete states of a class of continuous-time linear hybrid systems. We derive necessary and sufficient conditions that the structural parameters of the model must satisfy in order for filtering and smoothing algorithms to operate correctly. Our conditions are simple rank tests that exploit the geometry of the observability subspaces generated ...
متن کامل