相关论文: Logarithmic complete monotonicity of a matrix-para…

The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…

We study failure rate monotonicity and generalized convex transform stochastic ordering properties of random variables, with a concern on applications. We are especially interested in the effect of a tail weight iteration procedure to…

Given a collection $\{\lambda_1, \dots, \lambda_n\} $ of real numbers, there is a canonical probability distribution on the set of real symmetric or complex Hermitian matrices with eigenvalues $\lambda_1,\ldots,\lambda_n$. In this paper, we…

The translated logarithmic Lambert function is defined and basic analytic properties of the function are obtained including the derivative, integral, Taylor series expansion, real branches and asymptotic approximation of the function.…

In the paper, the authors discover an integral representation, some inequalities, and complete monotonicity of Bernoulli numbers of the second kind.

In this work, we establish a representation theorem for multivariable totally symmetric functions: a multisymmetric continuous function must be the composition of a continuous function and a set of generators of the multisymmetric…

We define a multidimensional rearrangement, which is related to classical inequalities for functions that are monotone in each variable. We prove the main measure theoretical results of the new theory and characterize the functional…

We present a formula for the trace of any symmetric power of a $n\times n$ matrix (with coefficients in a field) in terms of the ordinary powers of the matrix, an arbitrarily chosen linear function which vanishes on the identity matrix, and…

We consider the problem of jointly estimating multiple related zero-mean Gaussian distributions from data. We propose to jointly estimate these covariance matrices using Laplacian regularized stratified model fitting, which includes loss…

In the estimation of the mean matrix in a multivariate normal distribution, the generalized Bayes estimators with closed forms are provided, and the sufficient conditions for their minimaxity are derived relative to both matrix and scalar…

We study monotonicity and convexity properties of functions arising in the theory of elliptic integrals, and in particular in the case of a Schwarz-Christoffel conformal mapping from a half-plane to a trapezoid. We obtain sharp monotonicity…

Let $\mu$ be a probability measure on $\mathbb{R}$. We give conditions on the Fourier transform of its density for functionals of the form $H(a)=\int_{\mathbb{R}^n}h(\langle a,x\rangle)\mu^n(dx)$ to be Schur monotone. As applications, we…

We introduce and carefully study a natural probability measure over the numerical range of a complex matrix $A \in M_n(\C)$. This numerical measure $\mu_A$ can be defined as the law of the random variable $<AX,X> \in \C$ when the vector $X…

This is a short review of some recent results obtained by the author. These results are related the problem of obtaining polynomial identities (computational formulas) for some matrix functions by means of the known polarization theorem,…

We provide a new and simple characterization of the multivariate generalized Laplace distribution. In particular, this result implies that the product of a Gaussian matrix with independent and identically distributed columns by an…

Let $ f:(0,\infty)\rightarrow \Bbb{R} $ be a completely monotonic function. In this paper, we present some properties of this functions and several new classes of completely monotonic functions. We also give some special functions such that…

In this paper, we address the problem of estimating a covariance matrix of a multivariate Gaussian distribution, relative to a Stein loss function, from a decision theoretic point of view. We investigate the case where the covariance matrix…

The psi function $\psi(x)$ is defined by $\psi(x)=\frac{\Gamma'(x)}{\Gamma(x)}$ and $\psi^{(i)}(x)$ for $i\in\mathbb{N}$ denote the polygamma functions, where $\Gamma(x)$ is the gamma function. In this paper we prove that a function…

Algebraic tools in statistics have recently been receiving special attention and a number of interactions between algebraic geometry and computational statistics have been rapidly developing. This paper presents another such connection,…

We study the computability of the operator norm of a matrix with respect to norms induced by linear operators. Our findings reveal that this problem can be solved exactly in polynomial time in certain situations, and we discuss how it can…