Related papers: Asymptotic sequential Rademacher complexity of a f…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…
In this paper, we present the asymptotic distribution of M-estimators for parameters in non-stationary AR(p) processes. The innovations are assumed to be in the domain of attraction of a stable law with index $0<\alpha\le2$. In particular,…
The optimum quality that can be asymptotically achieved in the estimation of a probability p using inverse binomial sampling is addressed. A general definition of quality is used in terms of the risk associated with a loss function that…
We investigate measures of complexity of function classes based on continuity moduli of Gaussian and Rademacher processes. For Gaussian processes, we obtain bounds on the continuity modulus on the convex hull of a function class in terms of…
We prove an asymptotic formula for the number of orientations with given out-degree (score) sequence for a graph $G$. The graph $G$ is assumed to have average degrees at least $n^{1/3 + \varepsilon}$ for some $\varepsilon > 0$, and to have…
In random sequential covering, identical objects are deposited randomly, irreversibly, and sequentially; only attempts increasing the coverage are accepted. A finite system eventually gets congested, and we study the statistics of congested…
We prove the central limit theorem (CLT) for a sequence of independent zero-mean random variables $\xi_j$, perturbed by predictable multiplicative factors $\lambda_j$ with values in intervals $[\underline\lambda_j,\overline\lambda_j]$. It…
In this note we apply a lemma due to Sabach and Shtern to compute linear rates of asymptotic regularity for Halpern-type nonlinear iterations studied in optimization and nonlinear analysis.
In this paper, we present a novel method for computing the asymptotic values of both the optimal threshold, and the probability of success in sequences of optimal stopping problems. This method, based on the resolution of a first-order…
We consider second order differential equations with real coefficients that are in the limit circle case at infinity. Using the semiclassical Ansatz, we construct solutions (the Jost solutions) of such equations with a prescribed asymptotic…
A new approach to multi-dimensional quantum scattering by the infinite order discrete variable representation is presented. Determining the expansion coefficients of the wave function at the asymptotic regions by the solution of the…
In this paper we study satisfiability of random equations in an infinite finitely generated nilpotent group G. We show that the set SAT(G,k) of all equations in k > 1 variables over G which are satisfiable in G has an intermediate…
In this paper, we consider the distribution of the supremum of non-stationary Gaussian processes, and present a new theoretical result on the asymptotic behaviour of this distribution. Unlike previously known facts in this field, our main…
Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…
Asymptotic expansions are derived for associated Legendre functions of degree $\nu$ and order $\mu$, where one or the other of the parameters is large. The expansions are uniformly valid for unbounded real and complex values of the argument…
In this paper we study the randomized non-autonomous complete linear differential equation. The diffusion coefficient and the source term in the differential equation are assumed to be stochastic processes and the initial condition is…
The convergence of simultaneous and marginal predictive classifiers under partition exchangeability in supervised classification is obtained. The result shows the asymptotic convergence of these classifiers under infinite amount of training…
We consider a problem of approximation of $d$-variate functions defined on $\mathbb{R}^d$ which belong to the Hilbert space with tensor product-type reproducing Gaussian kernel with constant shape parameter. Within worst case setting, we…
The law of large numbers extends to random sets by employing Minkowski addition. Above that, a central limit theorem is available for set-valued random variables. The existing results use abstract isometries to describe convergence of the…
We present expressions for the coefficients which arise in asymptotic expansions of multiple integrals of Laplace type (the first term of which is known as Laplace's approximation) in terms of asymptotic series of the functions in the…