Related papers: Minimax-robust estimation problems for stationary …
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
An important estimation problem that is closely related to large-scale multiple testing is that of estimating the null density and the proportion of nonnull effects. A few estimators have been introduced in the literature; however, several…
We consider the detection problem of a two-dimensional function from noisy observations of its integrals over lines. We study both rate and sharp asymptotics for the error probabilities in the minimax setup. By construction, the derived…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
We develop a versatile framework for statistical learning in non-stationary environments. In each time period, our approach applies a stability principle to select a look-back window that maximizes the utilization of historical data while…
We consider the problem of estimating the value of a linear functional in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The…
In variational phase-field modeling of brittle fracture, the functional to be minimized is not convex, so that the necessary stationarity conditions of the functional may admit multiple solutions. The solution obtained in an actual…
Given a matrix the seriation problem consists in permuting its rows in such way that all its columns have the same shape, for example, they are monotone increasing. We propose a statistical approach to this problem where the matrix of…
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. In Johannes and Schenk [2010] it has been shown…
In this technical note, we deal with a spectrum approximation problem arising in THREE-like multivariate spectral estimation approaches. The solution to the problem minimizes a suitable divergence index with respect to an a priori spectral…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
Theory and algorithms are developed for detecting changes in the distribution of statistically periodic random processes. The statistical periodicity is modeled using independent and periodically identically distributed processes, a new…
We consider the problem of optimal linear estimation of the functional $$A_N \vec{\xi} =\sum_{j = 0}^{N} (\vec{a}(j))^{\top} \vec{\xi}(j)$$ that depends on the unknown values $\vec{\xi}(j),j=0,1,\dots,N,$ of a vector-valued harmonizable…
One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…
The paper is dealing with semi-classical asymptotics of a characteristic function for a stochastic process. The main technical tool is provided by the stationary phase method. The extremal range for a stochastic process is defined by limit…
Stochastic simulation models are generative models that mimic complex systems to help with decision-making. The reliability of these models heavily depends on well-calibrated input model parameters. However, in many practical scenarios,…
The dynamics of cellular chemical reactions are variable due to stochastic noise from intrinsic and extrinsic sources. The intrinsic noise is the intracellular fluctuations of molecular copy numbers caused by the probabilistic encounter 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…
In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…
This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…