Related papers: Explicit error bounds for lattice Edgeworth expans…
Wigner limits are given formally as the difference between a lattice sum, associated to a positive definite quadratic form, and a corresponding multiple integral. To define these limits, which arose in work of Wigner on the energy of static…
We prove error bounds in a central limit theorem for solutions of certain convolution equations. The main motivation for investigating these equations stems from applications to lace expansions, in particular to weakly self-avoiding random…
We obtain explicit bounds on the truncation error of the cumulant series of a bounded complex function of a random vector with independent components. The bounds are based on multidimensional differences. This extends the theory of the…
We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
In this article, we study the pointwise asymptotic behavior of iterated convolutions on the one dimensional lattice Z. We generalize the so-called local limit theorem in probability theory to complex valued sequences. A sharp rate of…
We consider information-theoretic bounds on expected generalization error for statistical learning problems in a networked setting. In this setting, there are $K$ nodes, each with its own independent dataset, and the models from each node…
This paper focuses on inhomogeneous quadratic tests, which involve the sum of a dependent non-central chi-square with a Gaussian random variable. Unfortunately, no closed-form expression is available for the statistical distribution of the…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
This paper is devoted to the estimators of the mean that provide strong non-asymptotic guarantees under minimal assumptions on the underlying distribution. The main ideas behind proposed techniques are based on bridging the notions of…
The Sinc quadrature and the Sinc indefinite integration are approximation formulas for definite integration and indefinite integration, respectively, which can be applied on any interval by using an appropriate variable transformation.…
The main result of this article is that we obtain an elementwise error bound for the Fused Lasso estimator for any general convex loss function $\rho$. We then focus on the special cases when either $\rho$ is the square loss function (for…
In this paper, we provide a new and sharper bound for the Legendre coefficients of differentiable functions and then derive a new error bound of the truncated Legendre series in the uniform norm. The key idea of proof relies on integration…
It has long been known how to construct radiation boundary conditions for the time dependent wave equation. Although arguments suggesting that they are accurate have been given, it is only recently that rigorous error bounds have been…
This paper explores the generalization characteristics of iterative learning algorithms with bounded updates for non-convex loss functions, employing information-theoretic techniques. Our key contribution is a novel bound for the…
We prove some inequalities involving fourth central moment of a random variable that takes values in a given finite interval. Both discrete and continuous cases are considered. Bounds for the spread are obtained when a given nxn complex…
Estimates are constructed for the deviation of the concentration functions of sums of independent random variables with finite variances from the folded normal distribution function without any assumptions concerning the existence of the…
In this work, we obtain decay bounds for a class of ID dispersive equations that includes the linearized water wave. These decay bounds display a surprising growth factor, which we show is sharp, The proofs rely on careful analysis of…
We study the problem of estimating the barycenter of a distribution given i.i.d. data in a geodesic space. Assuming an upper curvature bound in Alexandrov's sense and a support condition ensuring the strong geodesic convexity of the…
The MDL two-part coding $ \textit{index of resolvability} $ provides a finite-sample upper bound on the statistical risk of penalized likelihood estimators over countable models. However, the bound does not apply to unpenalized maximum…