Work

Detecting positive correlations in a multivariate sample

Year: 2015

Type: article

Abstract: We consider the problem of testing whether a correlation matrix of a multivariate normal population is the identity matrix. We focus on sparse classes of alternatives where only a few entries are nonzero and, in fact, positive. We derive a general lower bound applicable to various classes and study the performance of some near-optimal tests. We pay special attention to computational feasibility and construct near-optimal tests that can be computed efficiently. Finally, we apply our results to prove new lower bounds for the clique number of high-dimensional random geometric graphs.

Source: Bernoulli

DOI: 10.3150/13-bej565

Authors: Ery Arias-Castro, Sébastien Bubeck, Gábor Lugosi

Institutions: University of California San Diego, Princeton University, Universitat Pompeu Fabra

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, Ministerio de Ciencia y Tecnología, Office of Naval Research

Awards: G1046223130, G2103544611, G8876996369