Related papers: Pad\'e approximation for a multivariate Markov tra…
We extend known saddlepoint tail probability approximations to multivariate cases, including multivariate conditional cases. Our approximation applies to both continuous and lattice variables, and requires the existence of a cumulant…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…
The main purpose of this paper is to give a solution to a conjecture concerning a Pad\'{e} family of iterations for the matrix sector function that was recently raised by B. Laszkiewicz et al in [A Pad\'{e} family of iterations for the…
We provide sufficient conditions for quantitative convergence of the iterates of proximal splitting algorithms for minimizing a sum of functions on a metric space. The theory does not assume that the functions have common minima, nor does…
A novel application of the Pade approximation is proposed in which the Pade approximant is used as an interpolation for the small and large coupling behaviors of a physical system, resulting in a prediction of the behavior of the system at…
A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…
In this work, we consider the approximation of Hilbert space-valued meromorphic functions that arise as solution maps of parametric PDEs whose operator is the shift of an operator with normal and compact resolvent, e.g. the Helmholtz…
In this note we develop an extension of the Mar\v{c}enko-Pastur theorem to time series model with temporal correlations. The limiting spectral distribution (LSD) of the sample covariance matrix is characterised by an explicit equation for…
We view the classical Lindeberg principle in a Markov process setting to establish a probability approximation framework by the associated It\^{o}'s formula and Markov operator. As applications, we study the error bounds of the following…
In a variety of applications it is important to extract information from a probability measure $\mu$ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and possibly conditioned) continuous time…
The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…
We study the spectra of MANOVA estimators for variance component covariance matrices in multivariate random effects models. When the dimensionality of the observations is large and comparable to the number of realizations of each random…
We study a reliable pole selection for the rational approximation of the resolvent of fractional powers of operators in both the finite and infinite dimensional setting. The analysis exploits the representation in terms of hypergeometric…
A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…
The Stieltjes (or sometimes called the Cauchy) transform is a fundamental object associated with probability measures, corresponding to the generating function of the moments. In certain applications such as free probability it is essential…
In this paper, we explore quadratures for the evaluation of $B^T \phi(A) B$ where $A$ is a symmetric positive-definite (s.p.d.) matrix in $\mathbb{R}^{n \times n}$, $B$ is a tall matrix in $\mathbb{R}^{n \times p}$, and $\phi(\cdot)$…
This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We…
An approximate perturbed direct homotopy reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth order dispersion and second order dissipation. The similarity reduction equations are…
A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov…