相关论文: On Estimation of Isotonic Piecewise Constant Signa…

We consider the estimation of the value of a linear functional of the slope parameter in functional linear regression, where scalar responses are modeled in dependence of random functions. The theory in this paper covers in particular…

This paper discusses the possibility to find and construct \textit{piecewise constant martingales}, that is, martingales with piecewise constant sample paths evolving in a connected subset of $\mathbb{R}$. After a brief review of standard…

In the framework of nonparametric multivariate function estimation we are interested in structural adaptation. We assume that the function to be estimated has the "single-index" structure where neither the link function nor the index vector…

We deal with the problem of optimal estimation of the linear functionals constructed from the missed values of a continuous time stochastic process $\xi(t)$ with periodically stationary increments at points $t\in[0;(N+1)T]$ based on…

In this article, we consider the inverse problem of determining spatially heterogeneous absorption and diffusion coefficients from a single measurement of the absorbed energy (in the steady-state diffusion approximation of light transfer).…

We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…

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…

A central goal of causal inference is to detect and estimate the treatment effects of a given treatment or intervention on an outcome variable of interest, where a member known as the heterogeneous treatment effect (HTE) is of growing…

A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…

This article is devoted to nonlinear approximation and estimation via piecewise polynomials built on partitions into dyadic rectangles. The approximation rate is studied over possibly inhomogeneous and anisotropic smoothness classes that…

In this paper, we derive minimax rates for estimating both parametric and nonparametric components in partially linear additive models with high dimensional sparse vectors and smooth functional components. The minimax lower bound for…

In this paper, we propose the Minimum Regularized Covariance Trace (MRCT) estimator, a novel method for robust covariance estimation and functional outlier detection. The MRCT estimator employs a subset-based approach that prioritizes…

In this paper, we discuss the algorithm engineering aspects of an O(n^2)-time algorithm [6] for computing a minimum-area convex polygon that intersects a set of n isothetic line segments.

We study the rank of the instantaneous or spot covariance matrix $\Sigma_X(t)$ of a multidimensional continuous semi-martingale $X(t)$. Given high-frequency observations $X(i/n)$, $i=0,\ldots,n$, we test the null hypothesis…

We develop a general approach to estimating the derivative of a function-valued parameter $\theta_o(u)$ that is identified for every value of $u$ as the solution to a moment condition. This setup in particular covers many interesting models…

We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some…

We consider a misspecified optimization problem that requires minimizing of a convex function $f(x;\theta^*)$ in x over a constraint set represented by $h(x;\theta^*)\leq 0$, where $\theta^*$ is an unknown (or misspecified) vector of…

We introduce a penalty term-based splitting algorithm with inertial effects designed for solving monotone inclusion problems involving the sum of maximally monotone operators and the convex normal cone to the (nonempty) set of zeros of a…

This paper introduces a general regularized thresholded least-square procedure estimating a structured signal $\theta_*\in\mathbb{R}^d$ from the following observations: $y_i = f(\langle\mathbf{x}_i, \theta_*\rangle,…

We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…