Related papers: Minimax-robust estimation problems for stationary …

In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference…

Statistical inference for a linear stochastic hyperbolic equation with two unknown parameters is studied. Based on observation of coordinates of the solution or their linear combination, minimum contrast estimators are introduced. Strong…

In this article we consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises observed in discrete time moments. An adaptive model selection procedure is proposed. A sharp…

Complex systems are characterized by a huge number of degrees of freedom often interacting in a non-linear manner. In many cases macroscopic states, however, can be characterized by a small number of order parameters that obey stochastic…

We examine a fundamental problem that models various active sampling setups, such as network tomography. We analyze sampling of a multivariate normal distribution with an unknown expectation that needs to be estimated: in our setup it is…

We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…

The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…

The current paper presents a novel machinery for studying non-asymptotic minimax estimation of high-dimensional matrices, which yields tight minimax rates for a large collection of loss functions in a variety of problems. Based on the…

Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…

In this paper, we consider a functional linear regression model, where both the covariate and the response variable are functional random variables. We address the problem of optimal nonparametric estimation of the conditional expectation…

Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…

We develop a technique for establishing lower bounds on the sample complexity of Least Squares (or, Empirical Risk Minimization) for large classes of functions. As an application, we settle an open problem regarding optimality of Least…

This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…

We obtain minimax-optimal convergence rates in the supremum norm, including information-theoretic lower bounds, for estimating the covariance kernel of a stochastic process which is repeatedly observed at discrete, synchronous design…

This paper describes a new approach to solving some stochastic optimization problems for linear dynamic system with various parametric uncertainties. Proposed approach is based on application of tensor formalism for creation the…

We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model selection procedure is proposed. Under general moment conditions on the noise distribution a sharp…

Under mild Markov assumptions, sufficient conditions for strict minimax optimality of sequential tests for multiple hypotheses under distributional uncertainty are derived. First, the design of optimal sequential tests for simple hypotheses…

We consider uniform moment convergence of lag-window spectral density estimates for univariate and multivariate stationary processes. Optimal rates of convergence are obtained under mild and easily verifiable conditions. Our theory…

We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of second order stationary random functions X1,...,Xn. An orthogonal series estimator of…

This paper proposes a methodology to estimate characteristic functions of stochastic differential equations that are defined over polynomials and driven by L\'evy noise. For such systems, the time evolution of the characteristic function is…