Related papers: Computation of the expected value of a function of…
In this paper, we study the problem of estimating latent variable models with arbitrarily corrupted samples in high dimensional space ({\em i.e.,} $d\gg n$) where the underlying parameter is assumed to be sparse. Specifically, we propose a…
Simple proofs of the midpoint, trapezoidal and Simpson's rules are proved for numerical integration on a compact interval. The integrand is assumed to be twice continuously differentiable for the midpoint and trapezoidal rules, and to be…
We give a general statement of the convolution method so that one can provide explicit asymptotic estimations for all averages of square-free supported arithmetic functions that have a sufficiently regular order on the prime numbers and…
Motivated by various computational applications, we investigate the problem of estimating nested expectations. Building upon recent work by the authors, we propose a novel Monte Carlo estimator for nested expectations, inspired by sparse…
We present a new fractional Taylor formula for singular functions whose Caputo fractional derivatives are of bounded variation. It bridges and ``interpolates" the usual Taylor formulas with two consecutive integer orders. This enables us to…
We study the trapezoidal rule for periodic functions on uniform grids and show that the quadrature error exhibits a rich deterministic structure, beyond traditional asymptotic or statistical interpretations. Focusing on the prototype…
We derive computable upper bounds for the difference between an exact solution of the evolutionary convection-diffusion problem and an approximation of this solution. The estimates are obtained by certain transformations of the integral…
Generalized variational inference (GVI) provides an optimization-theoretic framework for statistical estimation that encapsulates many traditional estimation procedures. The typical GVI problem is to compute a distribution of parameters…
In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side \(F:\R^n\to\R^n\). When applied to such a problem the classical trapezoidal rule suffers from a loss of accuracy if…
We develop efficient numerical integration methods for computing an integral whose integrand is a product of a smooth function and the Gaussian function with a small standard deviation. Traditional numerical integration methods applied to…
A weighted likelihood technique for robust estimation of a multivariate Wrapped Normal distribution for data points scattered on a p-dimensional torus is proposed. The occurrence of outliers in the sample at hand can badly compromise…
Flexible estimation of the mean outcome under a treatment regimen (i.e., value function) is the key step toward personalized medicine. We define our target parameter as a conditional value function given a set of baseline covariates which…
Pearson's Chi-square test is a widely used tool for analyzing categorical data, yet its statistical power has remained theoretically underexplored. Due to the difficulties in obtaining its power function in the usual manner, Cochran (1952)…
The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled employing the fixed-stress…
Distributionally robust optimization (DRO) is a widely used framework for optimizing objective functionals in the presence of both randomness and model-form uncertainty. A key step in the practical solution of many DRO problems is a…
We study a new simple quadrature rule based on integrating a $C^1$ quadratic spline quasi-interpolant on a bounded interval. We give nodes and weights for uniform and non-uniform partitions. We also give error estimates for smooth functions…
The calculation of multivariate normal probabilities is of great importance in many statistical and economic applications. This paper proposes a spherical Monte Carlo method with both theoretical analysis and numerical simulation. First,…
The transition probability of a Cox-Ingersoll-Ross process can be represented by a non-central chi-square density. First we prove a new representation for the central chi-square density based on sums of powers of generalized Gaussian random…
Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples. An extreme-value copula is determined by its Pickands dependence function, which is a function on the unit simplex subject to…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…