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Likelihood ratio test for partial sphericity in high and ultra-high dimensions

By Liliana Maria Forzani, María Antonella Gieco and Carlos Tolmasky

Abstract

We consider, in the setting of p and n large, sample covariance matrices whose population counterparts follow a spiked population model, i.e., with the exception of the first (largest) few, all the population eigenvalues are equal. We study the asymptotic distribution of the partial maximum likelihood ratio statistic and use it to test for the dimension of the population spike subspace. Furthermore, we extend this to the ultra-high-dimensional case, i.e., p>;n. A thorough study of the power of the test gives a correction that allows us to test for the dimension of the population spike subspace even for values of the limit of p/n close to 1, a setting where other approaches have proved to be deficient.Fil: Forzani, Liliana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Litoral; ArgentinaFil: Gieco, María Antonella. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Litoral; ArgentinaFil: Tolmasky, Carlos. University of Minnesota; Estados Unido

Topics: HIGH-DIMENSIONAL STATISTICS, PRINCIPAL COMPONENT ANALYSIS, RANDOM MATRIX THEORY, SAMPLE COVARIANCE MATRIX, SPIKED POPULATION MODEL, Matemática Pura, Matemáticas, CIENCIAS NATURALES Y EXACTAS
Publisher: 'Elsevier BV'
Year: 2017
DOI identifier: 10.1016/j.jmva.2017.04.001
OAI identifier: oai:ri.conicet.gov.ar:11336/58592
Provided by: CONICET Digital
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