34 citations · 64 across the 22 of their papers we have counts for
16 papers · 1 filter
Non-asymptotic quantisation of spherically symmetric distributions
Luc Pronzato, Anatoly Zhigljavsky
Zador's celebrated theorem is a cornerstone of optimal quantisation, establishing both the weak limit of the empirical distribution of an -point optimal quantiser in and t…
Maximum mean discrepancies of Farey sequences
Toni Karvonen, Anatoly Zhigljavsky
We identify a large class of positive-semidefinite kernels for which a certain polynomial rate of convergence of maximum mean discrepancies of Farey sequences is equivalent to the…
Quasi-uniform designs with optimal and near-optimal uniformity constant
Luc Pronzato, Anatoly Zhigljavsky
A design is a collection of distinct points in a given set , which is assumed to be a compact subset of , and the mesh-ratio of a design is the ratio of its fill distance t…
Reproducing kernel Hilbert spaces, polynomials and the classical moment problems
Holger Dette, Anatoly Zhigljavsky
We show that polynomials do not belong to the reproducing kernel Hilbert space of infinitely differentiable translation-invariant kernels whose spectral measures have moments corre…
Random and quasi-random designs in group testing
Jack Noonan, Anatoly Zhigljavsky
For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random design…
Non-lattice covering and quanitization of high dimensional sets
Jack Noonan, Anatoly Zhigljavsky
The main problem considered in this paper is construction and theoretical study of efficient -point coverings of a -dimensional cube . Targeted values of are be…
Covering of high-dimensional cubes and quantization
Anatoly Zhigljavsky, Jack Noonan
As the main problem, we consider covering of a -dimensional cube by balls with reasonably large (10 or more) and reasonably small , like or . We do no…
Prediction in regression models with continuous observations
Holger Dette, Andrey Pepelyshev, Anatoly Zhigljavsky
We consider the problem of predicting values of a random process or field satisfying a linear model , where errors are correlate…
Approximations for the boundary crossing probabilities of moving sums of random variables
Jack Noonan, Anatoly Zhigljavsky
In this paper we study approximations for the boundary crossing probabilities of moving sums of i.i.d. normal r.v. We approximate a discrete time problem with a continuous time pro…
Approximations for the boundary crossing probabilities of moving sums of normal random variables
Jack Noonan, Anatoly Zhigljavsky
In this paper we study approximations for boundary crossing probabilities for the moving sums of i.i.d. normal random variables. We propose approximating a discrete time problem wi…
Bregman divergences based on optimal design criteria and simplicial measures of dispersion
Luc Pronzato, Henry Wynn, Anatoly Zhigljavsky
In previous work the authors defined the k-th order simplicial distance between probability distributions which arises naturally from a measure of dispersion based on the squared v…
Bayesian quadrature and energy minimization for space-filling design
Luc Pronzato, Anatoly Zhigljavsky
A standard objective in computer experiments is to approximate the behaviour of an unknown function on a compact domain from a few evaluations inside the domain. When little is kno…
Optimal designs for regression models with autoregressive errors structure
Holger Dette, Andrey Pepelyshev, Anatoly Zhigljavsky
In the one-parameter regression model with AR(1) and AR(2) errors we find explicit expressions and a continuous approximation of the optimal discrete design for the signed least sq…
An extended Generalised Variance, with Applications
Luc Pronzato, Henry Wynn, Anatoly Zhigljavsky
We consider a measure k of dispersion which extends the notion of Wilk's generalised variance, or entropy, for a d-dimensional distribution, and is based on the mean squared vo…
Optimal design for linear models with correlated observations
Holger Dette, Andrey Pepelyshev, Anatoly Zhigljavsky
In the common linear regression model the problem of determining optimal designs for least squares estimation is considered in the case where the observations are correlated. A nec…
Asymptotic optimal designs under long-range dependence error structure
Holger Dette, Nikolai Leonenko, Andrey Pepelyshev +1
We discuss the optimal design problem in regression models with long-range dependence error structure. Asymptotic optimal designs are derived and it is demonstrated that these desi…