Related papers: Uniformity and the delta method
We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional…
Decision makers may suffer from uncertainty induced by limited data. This may be mitigated by accounting for epistemic uncertainty, which is however challenging to estimate efficiently for large neural networks. To this extent we…
We find asymptotic equalities for exact upper bounds of approximations by Fourier sums in uniform metric on classes of $2\pi$-periodic functions, representable in the form of convolutions of functions $\varphi$, which belong to unit balls…
The first goal of this paper is to study necessary and sufficient conditions to obtain the attainability of the \textit{fractional Hardy inequality } $$\Lambda_{N}\equiv\Lambda_{N}(\Omega):=\inf_{\{\phi\in \mathbb{E}^s(\Omega, D), \phi\neq…
We discuss in this paper uniform exponential convergence of sample average approximation (SAA) with adaptive multiple importance sampling (AMIS) and asymptotics of its optimal value. Using a concentration inequality for bounded martingale…
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…
Asymptotic optimality is a key theoretical property in model averaging. Due to technical difficulties, existing studies rely on restricted weight sets or the assumption that there is no true model with fixed dimensions in the candidate set.…
We consider a class of wave equations with constant damping and polynomial nonlinearities that are perturbed by small, multiplicative, space-time white noise. The equations are defined on a one-dimensional bounded interval with Dirichlet…
We analyze the conforming approximation of the time-harmonic Maxwell's equations using N\'ed\'elec (edge) finite elements. We prove that the approximation is asymptotically optimal, i.e., the approximation error in the energy norm is…
In this paper we complement the program concerning the application of symmetrization methods to nonlocal PDEs by providing new estimates, in the sense of mass concentration comparison, for solutions to linear fractional elliptic and…
By application of the theory for second-order linear differential equations with two turning points developed in [Olver F.W.J., Philos. Trans. Roy. Soc. London Ser. A 278 (1975), 137-174], uniform asymptotic approximations are obtained in…
The article addresses the convergence of implicit and semi-implicit, fully discrete approximations of a class of nonlinear parabolic evolution problems. Such schemes are popular in the numerical solution of evolutions defined with the…
We study the homogeneous Dirichlet problem for the doubly nonlinear equation $u_t = \Delta_p u^m$, where $p>1,\ m>0$ posed in a bounded domain in $\mathbb{R}^N$ with homogeneous boundary conditions and with non-negative and integrable data.…
For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…
In the uniformity testing task, an algorithm is provided with samples from an unknown probability distribution over a (known) finite domain, and must decide whether it is the uniform distribution, or, alternatively, if its total variation…
We give an extension of a criterion of van der Corput on uniform distribution of sequences. Namely, we prove that a sequence $x_n$ is uniformly distributed modulo 1 if it is weakly monotonic and satisfies the conditions $\Delta^2x_n\to…
The telegraph process $\{X(t), t>0\}$, is supposed to be observed at $n+1$ equidistant time points $t_i=i\Delta_n,i=0,1,..., n$. The unknown value of $\lambda$, the underlying rate of the Poisson process, is a parameter to be estimated. The…
We consider positive solutions, possibly unbounded, to the semilinear equation $-\Delta u=f(u)$ on continuous epigraphs bounded from below. Under the homogeneous Dirichlet boundary condition, we prove new monotonicity results for $u$, when…