Related papers: Minimax Optimal Additive Functional Estimation wit…
The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…
This paper is devoted to the a posteriori error analysis of multiharmonic finite element approximations to distributed optimal control problems with time-periodic state equations of parabolic type. We derive a posteriori estimates of…
We re-visit the classical problem of optimal payment of dividends and determine the degree to which the diffusion approximation serves as a valid approximation of the classical risk model for this problem. Our results parallel some of those…
This paper considers adaptive, minimax estimation of a quadratic functional in a nonparametric instrumental variables (NPIV) model, which is an important problem in optimal estimation of a nonlinear functional of an ill-posed inverse…
We study the fundamental problem of estimating an unknown discrete distribution $p$ over $d$ symbols, given $n$ i.i.d. samples from the distribution. We are interested in minimizing the KL divergence between the true distribution and the…
This survey provides an overview of optimal estimation of linear functionals which depend on the unknown values of a stationary stochastic sequence. Based on observations of the sequence without noise as well as observations of the sequence…
What is the fastest possible "diffusion"? A trivial answer would be "a process that converts a Dirac delta-function into a uniform distribution infinitely fast". Below, we consider a more reasonable formulation: a process that maximizes…
We find uniform with respect to parameter $p \ (1\leq p\leq\infty)$ upper estimations of best approximations by trigonometric polynomials of classes $C^{\psi}_{\beta,p}$ of periodic functions generated by sequences $\psi(k)$, that decrease…
Let $\cF$ be a set of $M$ classification procedures with values in $[-1,1]$. Given a loss function, we want to construct a procedure which mimics at the best possible rate the best procedure in $\cF$. This fastest rate is called optimal…
A crucial feature of reaction-diffusion epidemic models is the incidence function, which characterizes disease transmission dynamics. Over the past few decades, many studies have investigated the behavior of such models under various…
The problem of the mean-square optimal linear estimation of functionals which depend on the unknown values of a stationary stochastic sequence from observations of the sequence with noise is considered. In the case of spectral certainty,…
We provide a decision theoretic analysis of bandit experiments under local asymptotics. Working within the framework of diffusion processes, we define suitable notions of asymptotic Bayes and minimax risk for these experiments. For normally…
We deal with the problem of optimal estimation of the linear functionals constructed from unobserved values of a continuous time stochastic process with periodically correlated increments based on past observations of this process. To solve…
In this paper we introduce the concept of additive approximation schemes and apply it to load balancing problems. Additive approximation schemes aim to find a solution with an absolute error in the objective of at most $\epsilon h$ for some…
Motivated by applications to prediction and forecasting, we suggest methods for approximating the conditional distribution function of a random variable Y given a dependent random d-vector X. The idea is to estimate not the distribution of…
We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…
We present a systematic study of the reconstruction of a non-negative function via maximum entropy approach utilizing the information contained in a finite number of moments of the function. For testing the efficacy of the approach, we…
In this paper, we propose a new lower approximation scheme for POMDP with discounted and average cost criterion. The approximating functions are determined by their values at a finite number of belief points, and can be computed efficiently…
The problem of computing functions of values at the nodes in a network in a totally distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer,…
Feedback particle filter (FPF) is a numerical algorithm to approximate the solution of the nonlinear filtering problem in continuous-time settings. In any numerical implementation of the FPF algorithm, the main challenge is to numerically…