Inhaltszusammenfassung

The Gaussian product inequality (GPI) is an important conjecture concerning the moments of Gaussian random vectors. Numerous partial results have been derived in recent decades and we provide here further results on the problem. We establish a strong version of the GPI for multivariate gamma distributions in the case of nonnegative correlations, thereby extending a result recently derived by Genest and Quimet [5]. Further, we show that the GPI holds with nonnegative exponents for all rand...The Gaussian product inequality (GPI) is an important conjecture concerning the moments of Gaussian random vectors. Numerous partial results have been derived in recent decades and we provide here further results on the problem. We establish a strong version of the GPI for multivariate gamma distributions in the case of nonnegative correlations, thereby extending a result recently derived by Genest and Quimet [5]. Further, we show that the GPI holds with nonnegative exponents for all random vectors with positive components whenever the underlying vector is positively upper orthant dependent. Finally, we show that the GPI with negative exponents follows directly from the Gaussian correlation inequality, which was proved by Royen [14]. » weiterlesen» einklappen

Autoren

Klassifikation

DFG Fachgebiet:
Mathematik

DDC Sachgruppe:
Statistik