Related papers: Near-optimal mean value estimates for multidimensi…
We estimate from above and below the dimension of invariant measure for contracting-on-average iterated function systems in $\R^d$.
In this paper, we develop interval estimation methods for means of bounded random variables based on a sequential procedure such that the sampling is continued until the sample sum is no less than a prescribed threshold.
This paper proves nontrivial bounds for short mixed character sums by introducing estimates for Vinogradov's mean value theorem into a version of the Burgess method.
Estimation of mutual information between (multidimensional) real-valued variables is used in analysis of complex systems, biological systems, and recently also quantum systems. This estimation is a hard problem, and universally good…
We give an effective version with explicit constants of a mean value theorem of Vaughan related to the values of \psi(y, \chi), the twisted summatory function associated to the von Mangoldt function \Lambda and a Dirichlet character \chi.…
In this paper we extend the refined second-order Poincar\'e inequality for Poisson functionals from a one-dimensional to a multi-dimensional setting. Its proof is based on a multivariate version of the Malliavin-Stein method for normal…
In this paper, we address the problem of approximating a multivariate function defined on a general domain in $d$ dimensions from sample points. We consider weighted least-squares approximation in an arbitrary finite-dimensional space $P$…
In this paper, we study multivariate vector sampling expansions on general finitely generated shift-invariant subspaces. Necessary and sufficient conditions for a multivariate vector sampling theorem to hold are given.
We establish effective mean-value estimates for a wide class of multiplicative arithmetic functions, thereby providing (essentially optimal) quantitative versions of Wirsing's classical estimates and extending those of Hal\'asz. Several…
Models which include domain constraints occur in myriad contexts such as econometrics, genomics, and environmetrics, though simulating from constrained distributions can be computationally expensive. In particular, repeated sampling from…
The main results extend to sums over primes in a short interval earlier estimates by the author for "long" Weyl sums over primes.
Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…
Given an isometry invariant valuation on a complex space form we compute its value on the tubes of sufficiently small radii around a set of positive reach. This generalizes classical formulas of Weyl, Gray and others about the volume of…
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
We establish two theorems for assessing the accuracy in total variation of multivariate discrete normal approximation to the distribution of an integer valued random vector $W$. The first is for sums of random vectors whose dependence…
We consider an extremal problem for polynomials, which is dual to the well-known Smale mean value problem. We give a rough estimate depending only on the degree.
Using the adjoint action of the infinitesimal translations (with respect to some (in)dependant variables) on specific finite-dimensional subspaces of the space of generalized symmetries of some system of partial differential equations, we…
Understanding generalization is crucial to confidently engineer and deploy machine learning models, especially when deployment implies a shift in the data domain. For such domain adaptation problems, we seek generalization bounds which are…