info:eu-repo/semantics/article
Orthant probabilities and the attainment of maxima on a vertex of a simplex
Fecha
2021-02Registro en:
Pinasco, Damian; Smucler, Ezequiel; Zalduendo, Ignacio Martin; Orthant probabilities and the attainment of maxima on a vertex of a simplex; Elsevier; Linear Algebra and its Applications; 610; 2-2021; 785-803
0024-3795
CONICET Digital
CONICET
Autor
Pinasco, Damian
Smucler, Ezequiel
Zalduendo, Ignacio Martin
Resumen
We calculate bounds for orthant probabilities for the equicorrelated multivariate normal distribution and use these bounds to show the following: for degree k>4, the probability that a k-homogeneous polynomial in n variables attains a local constrained maximum on a vertex of the n-dimensional simplex tends to one as the dimension n grows. The bounds we obtain for the orthant probabilities are tight up to log(n) factors.