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The subject of this paper is the problem of nonparametric estimation of a continuous distribution function from observations with measurement errors. We study minimax complexity of this problem when unknown distribution has a density…
We consider the problem of estimating the slope function in a functional regression with a scalar response and a functional covariate. This central problem of functional data analysis is well known to be ill-posed, thus requiring a…
We study the problem of the nonparametric estimation for the density $\pi$ of the stationary distribution of a $d$-dimensional stochastic differential equation $(X_t)_{t \in [0, T]}$. From the continuous observation of the sampling path on…
We consider the problem of estimation of a linear functional in the Gaussian sequence model where the unknown vector theta in R^d belongs to a class of s-sparse vectors with unknown s. We suggest an adaptive estimator achieving a…
For nonparametric regression with one-sided errors and a boundary curve model for Poisson point processes we consider the problem of efficient estimation for linear functionals. The minimax optimal rate is obtained by an unbiased estimation…
Functional covariates are common in many medical, biodemographic, and neuroimaging studies. The aim of this paper is to study functional Cox models with right-censored data in the presence of both functional and scalar covariates. We study…
We consider the problem of estimating the asymptotic variance of a function defined on a Markov chain, an important step for statistical inference of the stationary mean. We design a novel recursive estimator that requires $O(1)$…
We consider a non-stationary sequential stochastic optimization problem, in which the underlying cost functions change over time under a variation budget constraint. We propose an $L_{p,q}$-variation functional to quantify the change, which…
We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the risk of the selected estimator with…
The approximation of smooth functions with a spectral basis typically leads to rapidly decaying coefficients where the rate of decay depends on the smoothness of the function and vice-versa. The optimal number of degrees of freedom in the…
This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…
In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations…
We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but whose joint distribution is not. We establish and exploit an…
We formulate the problem of numerical analytic continuation in a way that lets us draw meaningful conclusions about properties of the spectral function based solely on the input data. Apart from ensuring consistency with the input data…
In this paper, we study estimation of certain integral functionals of one or two densities with samples from stationary m-dependent sequences. We consider two types of U-statistic estimators for these functionals that are functions of the…
This paper concerns a spectral estimation problem for multivariate (i.e., vector-valued) signals defined on a multidimensional domain, abbreviated as M$^2$. The problem is posed as solving a finite number of trigonometric moment equations…
We propose a model selection approach for covariance estimation of a multi-dimensional stochastic process. Under very general assumptions, observing i.i.d replications of the process at fixed observation points, we construct an estimator of…
We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…
We consider spatially extended conductance based neuronal models with noise described by a stochastic reaction diffusion equation with additive noise coupled to a control variable with multiplicative noise but no diffusion. We only assume a…
Estimation problems with constrained parameter spaces arise in various settings. In many of these problems, the observations available to the statistician can be modelled as arising from the noisy realization of the image of a random linear…