Related papers: Generalized Bernstein-type approximation of contin…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
We provide a simple explicit estimator for discretely observed Barndorff-Nielsen and Shephard models, prove rigorously consistency and asymptotic normality based on the single assumption that all moments of the stationary distribution of…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
This paper is concerned with general nonlinear regression models where the predictor variables are subject to Berkson-type measurement errors. The measurement errors are assumed to have a general parametric distribution, which is not…
This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial…
Statistical inference can be performed by minimizing, over the parameter space, the Wasserstein distance between model distributions and the empirical distribution of the data. We study asymptotic properties of such minimum Wasserstein…
We present an exact Bayesian inference method for discrete statistical models, which can find exact solutions to a large class of discrete inference problems, even with infinite support and continuous priors. To express such models, we…
In this paper we introduce a new family of Bernstein-type exponential polynomials on the hypercube $[0, 1]^d$ and study their approximation properties. Such operators fix a multidimensional version of the exponential function and its…
Method of parameterizing and smoothing the unknown underling distributions using Bernstein polynomials is proposed, verified and investigated. Any distribution with bounded and smooth enough density can be approximated by the proposed…
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
In this paper we establish the accuracy and robustness of a fast estimator for the bispectrum - the "FFT bispectrum estimator". The implementation of the estimator presented here offers speed and simplicity benefits over a direct sampling…
In the frequentist program, inferential methods with exact control on error rates are a primary focus. The standard approach, however, is to rely on asymptotic approximations, which may not be suitable. This paper presents a general…
In this paper we provide new several Jackson-type approximations results for continuous fuzzy-number-valued functions which improve several previous ones. We use alternative techniques adapted from Interval Analysis which rely on the…
We consider the approximation of manifold-valued functions by embedding the manifold into a higher dimensional space, applying a vector-valued approximation operator and projecting the resulting vector back to the manifold. It is well known…
In this paper a semidiscrete Fourier pseudospectral method for approximating Benjamin-type equations is introduced and analyzed. A study of convergence is presented.
A representation for the sharp coefficient in a pointwise estimate for the gradient of a generalized Poisson integral of a function $f$ on ${\mathbb R}^{n-1}$ is obtained under the assumption that $f$ belongs to $L^p$. It is assumed that…
The major contributions of this paper lie in two aspects. Firstly, we focus on deriving Bernstein-type inequalities for both geometric and algebraic irregularly-spaced NED random fields, which contain time series as special case.…
This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical…
Shape restrictions on functional regression coefficients such as non-negativity, monotonicity, convexity or concavity are often available in the form of a prior knowledge or required to maintain a structural consistency in functional…
The main aim of this paper is to further develop the multiple-correction method that formulated in our previous works~\cite{CXY, Cao}. As its applications, we establish a kind of hybrid-type finite continued fraction approximations related…