相关论文: Robust Estimation through Schoenberg transformatio…

It is well-known that adaptive homodyne estimation of continuously varying optical phase provides superior accuracy in the phase estimate as compared to adaptive or non-adaptive static estimation. However, most phase estimation schemes rely…

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

For the two-dimensional Schr\"odinger equation, the general form of the point transformations such that the result can be interpreted as a Schr\"odinger equation with effective (i.e. position dependent) mass is studied. A wide class of such…

The problem of the recovery of a real-valued potential in the two-dimensional Schrodinger equation at positive energy from the Dirichlet-to-Neumann map is considered. It is know that this problem is severely ill-posed and the reconstruction…

We study stochastic evolution equations describing the dynamics of open quantum systems. First, using resolvent approximations, we obtain a sufficient condition for regularity of solutions to linear stochastic Schroedinger equations driven…

Economists often estimate economic models on data and use the point estimates as a stand-in for the truth when studying the model's implications for optimal decision-making. This practice ignores model ambiguity, exposes the decision…

Robust optimization is a tractable and expressive technique for decision-making under uncertainty, but it can lead to overly conservative decisions when pessimistic assumptions are made on the uncertain parameters. Wasserstein…

While the traditional viewpoint in machine learning and statistics assumes training and testing samples come from the same population, practice belies this fiction. One strategy -- coming from robust statistics and optimization -- is thus…

We propose a scalable robust learning algorithm combining kernel smoothing and robust optimization. Our method is motivated by the convex analysis perspective of distributionally robust optimization based on probability metrics, such as the…

Robust estimators and Wald-type tests are developed for the multinomial logistic regression based on $\phi$-divergence measures. The robustness of the proposed estimators and tests is proved through the study of their influence functions…

This chapter presents an introduction to robust statistics with applications of a chemometric nature. Following a description of the basic ideas and concepts behind robust statistics, including how robust estimators can be conceived, the…

We consider the inverse problem of determining initial data in general Ornstein-Uhlenbeck equations on the Euclidean space from partial measurement localized on the so-called thick sets. Using the logarithmic convexity technique and recent…

The aim of this paper is to investigate the response of this system/scheme in terms of stability in presence of explicitly treated residual terms, as it inevitably occurs in the reality of NWP. This sudy is restricted to the impact of…

Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…

We provide a new computationally-efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models: in the classical Huber epsilon-contamination model and in heavy-tailed settings.…

Reliable inference for spatial regression remains challenging because it requires the correct specification of the spatial dependence structure, the mean trend, and the error distribution. Existing parametric testing methods rely on…

This article studies the \emph{robust covariance matrix estimation} of a data collection $X = (x_1,\ldots,x_n)$ with $x_i = \sqrt \tau_i z_i + m$, where $z_i \in \mathbb R^p$ is a \textit{concentrated vector} (e.g., an elliptical random…

This paper studies robust regression for data on Riemannian manifolds. Geodesic regression is the generalization of linear regression to a setting with a manifold-valued dependent variable and one or more real-valued independent variables.…

Multidimensional persistence studies topological features of shapes by analyzing the lower level sets of vector-valued functions. The rank invariant completely determines the multidimensional analogue of persistent homology groups. We prove…

A main goal in the field of statistical shape analysis is to define computable and informative metrics on spaces of immersed manifolds, such as the space of curves in a Euclidean space. The approach taken in the elastic shape analysis…