Related papers: Testing the disjunction hypothesis using Voronoi d…
Power-enhanced tests with high-dimensional data have received growing attention in theoretical and applied statistics in recent years. Existing tests possess their respective high-power regions, and we may lack prior knowledge about the…
In this article, we consider the problem of simultaneous testing of hypotheses when the individual test statistics are not necessarily independent. Specifically, we consider the problem of simultaneous testing of point null hypotheses…
Although several nonparametric tests are available for testing population identical distributions or equal means in multiple groups problem, the Van der Waerden test has asymptotically the same efficiency as the classical one-way analysis…
The wide availability of biological data at the genome-scale and across multiple variables has resulted in statistical questions regarding the enrichment or depletion of the number of discrete objects (e.g. genes) identified in individual…
Poisson Voronoi tessellations have been used in modeling many types of systems across different sciences, from geography and astronomy to telecommunications. The existing literature on the statistical properties of Poisson Voronoi cells is…
Minimization diagrams encompass a large class of diagrams of interest in the literature, such as generalized Voronoi diagrams. We develop an abstract perturbation theory and perform a sensitivity analysis for functions depending on sets…
A topological multiple testing approach to peak detection is proposed for the problem of detecting transcription factor binding sites in ChIP-Seq data. After kernel smoothing of the tag counts over the genome, the presence of a peak is…
We study Voronoi diagrams for distance functions that add together two convex functions, each taking as its argument the difference between Cartesian coordinates of two planar points. When the functions do not grow too quickly, then the…
In a high dimensional regression setting in which the number of variables ($p$) is much larger than the sample size ($n$), the number of possible two-way interactions between the variables is immense. If the number of variables is in the…
We present an extension of Voronoi diagrams where when considering which site a client is going to use, in addition to the site distances, other site attributes are also considered (for example, prices or weights). A cell in this diagram is…
Let $X$ be a Poisson point process and $K\subset\mathbb{R}^d$ a measurable set. Construct the Voronoi cells of all points $x\in X$ with respect to $X$, and denote by $v_X(K)$ the union of all Voronoi cells with nucleus in $K$. For $K$ a…
Thanks to its favorable properties, the multivariate normal distribution is still largely employed for modeling phenomena in various scientific fields. However, when the number of components $p$ is of the same asymptotic order as the sample…
This study proposes an innovative approach to analyze spatial patterns of behavior by integrating information in weighted Voronoi diagrams. The objective of the research is to analyze the temporal distribution of an experimental subject in…
The identification of predefined groups of genes ("gene-sets") which are differentially expressed between two conditions ("gene-set analysis", or GSA) is a very popular analysis in bioinformatics. GSA incorporates biological knowledge by…
Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under…
Research on the localization of the genetic basis associated with diseases or traits has been widely conducted in the last a few decades. Scan methods have been developed for region-based analysis in whole-genome association studies,…
Any system of bisectors (in the sense of abstract Voronoi diagrams) defines an arrangement of simple curves in the plane. We define Voronoi-like graphs on such an arrangement, which are graphs whose vertices are locally Voronoi. A vertex…
A novel algorithm to detect coherent structures with sparse Lagrangian particle tracking data, using Voronoi tessellation and techniques from spectral graph theory, is tested. Neighbouring tracer particles are naturally identified through…
High-dimensional phenotypes hold promise for richer findings in association studies, but testing of several phenotype traits aggravates the grand challenge of association studies, that of multiple testing. Several methods have recently been…
Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however so far only with flat hypersurfaces as cell-cell contact borders. In order to reproduce the experimentally…