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B0704
Title: Likelihood ratio test for partial sphericity in high and ultra-high dimensions Authors:  Maria Antonella Gieco - CONICET - Facultad de Ingenieria Quimica, UNL (Argentina) [presenting]
Liliana Forzani - Universidad Nacional del Litoral (Argentina)
Carlos Tolmasky - University of Minnesota (United States)
Abstract: The spiked population model for covariance matrices is revisited in the setting of $p$ and $n$ large. This model assumes that all the population eigenvalues, with the exception of the first (largest) few, are all equal. The asymptotic distribution of the partial likelihood ratio statistic is studied and used to test for the dimension of the spike subspace. The analysis is extended to the ultra-high dimensional case, i.e. $p>n$. A thorough study of the power of the test gives a correction that allows to test for the dimension of the spike subspace even for values of $p/n$ close to $1$, a setting where other approaches proved to be deficient.