Zobrazeno 1 - 10
of 307
pro vyhledávání: '"Richards, Donald P."'
For a given positive integer $m$, the concept of {\it hyperdeterminantal total positivity} is defined for a kernel $K:\R^{2m} \to \R$, thereby generalizing the classical concept of total positivity. Extending the fundamental example, $K(x,y) = \exp(x
Externí odkaz:
http://arxiv.org/abs/2412.03000
Publikováno v:
Proceedings of the American Mathematical Society (2025)
This paper provides the first explicit formula for the expectation of the product of two disjoint principal minors of a Wishart random matrix, solving a part of a broader problem put forth by Samuel S. Wilks in 1934 in the Annals of Mathematics. The
Externí odkaz:
http://arxiv.org/abs/2409.14512
Publikováno v:
Stat (2024), 13 (2), e706, 6 pp
In 1934, the American statistician Samuel S. Wilks derived remarkable formulas for the joint moments of embedded principal minors of sample covariance matrices in multivariate Gaussian populations, and he used them to compute the moments of sample st
Externí odkaz:
http://arxiv.org/abs/2403.06330
Autor:
Bagyan, Armine, Richards, Donald
Publikováno v:
SIGMA 20 (2024), 094, 22 pages
For positive integers $d$ and $p$ such that $d \ge p$, let $\mathbb{R}^{d \times p}$ denote the set of $d \times p$ real matrices, $I_p$ be the identity matrix of order $p$, and $V_{d,p} = \{x \in \mathbb{R}^{d \times p} \mid x'x = I_p\}$ be the Stie
Externí odkaz:
http://arxiv.org/abs/2402.08663
The B-spline copula function is defined by a linear combination of elements of the normalized B-spline basis. We develop a modified EM algorithm, to maximize the penalized pseudo-likelihood function, wherein we use the smoothly clipped absolute devia
Externí odkaz:
http://arxiv.org/abs/2402.07569
Publikováno v:
Electronic Journal of Probability (2024), 29, 1-26
This paper extends various results related to the Gaussian product inequality (GPI) conjecture to the setting of disjoint principal minors of Wishart random matrices. This includes product-type inequalities for matrix-variate analogs of completely mo
Externí odkaz:
http://arxiv.org/abs/2311.00202
Autor:
Bagyan, Armine, Richards, Donald
For $d \ge 2$, let $X$ be a random vector having a Bingham distribution on $\mathcal{S}^{d-1}$, the unit sphere centered at the origin in $\R^d$, and let $\Sigma$ denote the symmetric matrix parameter of the distribution. Let $\Psi(\Sigma)$ be the no
Externí odkaz:
http://arxiv.org/abs/2303.10290
We consider the truncated multivariate normal distributions for which every component is one-sided truncated. We show that this family of distributions is an exponential family. We identify $\mathcal{D}$, the corresponding natural parameter space, an
Externí odkaz:
http://arxiv.org/abs/2303.10287
Autor:
Bagyan, Armine, Richards, Donald
Since late 2019 the novel coronavirus, also known as COVID-19, has caused a pandemic that persists. This paper shows how a continuous-time Markov chain model for the spread of COVID-19 can be used to explain, and justify to undergraduate students, st
Externí odkaz:
http://arxiv.org/abs/2206.10179
Autor:
Bagyan, Armine, Richards, Donald
We consider random walks on the cone of $m \times m$ positive definite matrices, where the underlying random matrices have orthogonally invariant distributions on the cone and the Riemannian metric is the measure of distance on the cone. By applying
Externí odkaz:
http://arxiv.org/abs/2206.10138