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On a conjecture of Lamkin and Tkocz: Log-convexity of moments of Bernoulli sample means
Frédéric Ouimet, Frédéric Ouimet
Let be independent random variables, and let . We prove that, for every real , the sequenc…
Log-convexity and log-concavity of noncentral gamma sums and differences
Robert E. Gaunt, Frédéric Ouimet
We study log-convexity and log-concavity of densities obtained from sums and differences of two independent noncentral gamma random variables. We give a complete classification of…
On Wilks' problem: Exact recursive formulas via Stein's method for the joint moments of disjoint principal minors of Wishart random matrices
Robert E. Gaunt, Frédéric Ouimet
In a 1934 Annals of Mathematics paper, Samuel S. Wilks posed the problem of computing joint moments of disjoint principal minors of Wishart random matrices, describing the general…
Stein's method for the symmetric matrix normal distribution with an application to the approximation of the Wishart law
Robert E. Gaunt, Frédéric Ouimet
In this paper, we extend Stein's method to the symmetric matrix normal distribution. In particular, we obtain a Stein characterization of the symmetric matrix normal distribution i…
Stein's method for the Wishart distribution
Gabriel Bailly, Robert E. Gaunt, Frédéric Ouimet +2
In this work, we develop Stein's method for the Wishart distribution on the cone of positive definite matrices. We establish the basic ingredients of a Wishart Stein framework: we…
Results related to the Gaussian product inequality conjecture for mixed-sign exponents in arbitrary dimension
Guolie Lan, Frédéric Ouimet, Wei Sun
This note establishes that the opposite Gaussian product inequality (GPI) of the type proved by Russell & Sun (2022a) in two dimensions, and partially extended to higher dimensions…