Related papers: The Neyman-Pearson lemma for convex expectations
In this paper, we discuss the ambiguous chance constrained based portfolio optimization problems, in which the perturbations associated with the input parameters are stochastic in nature, but their distributions are not known precisely. We…
This paper provides an overview of results and concepts in minimax robust hypothesis testing for two and multiple hypotheses. It starts with an introduction to the subject, highlighting its connection to other areas of robust statistics and…
Most existing binary classification methods target on the optimization of the overall classification risk and may fail to serve some real-world applications such as cancer diagnosis, where users are more concerned with the risk of…
This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the…
In this paper, we study a discrete-time stochastic optimal control problem under distribution uncertainty with convex control domain. By weak convergence method and Sion's minimax theorem, we obtain the variational inequality for cost…
In this paper, we propose a novel method for matrix completion under general non-uniform missing structures. By controlling an upper bound of a novel balancing error, we construct weights that can actively adjust for the non-uniformity in…
Let $F$ be a finite model of cardinality $M$ and denote by $\operatorname {conv}(F)$ its convex hull. The problem of convex aggregation is to construct a procedure having a risk as close as possible to the minimal risk over $\operatorname…
We study the problem of testing the goodness of fit of categorical count data to a Poisson distribution uniform over the categories, against a class of alternatives defined by excluding an $\ell_p$ ball, $p \leq 2$, of radius $\epsilon$…
Based on two independent samples X_1,...,X_m and X_{m+1},...,X_n drawn from multivariate distributions with unknown Lebesgue densities p and q respectively, we propose an exact multiple test in order to identify simultaneously regions of…
Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from…
The main purpose of this paper is to provide an asymptotically optimal test. The proposed statistic is of Neyman-Pearson-type when the parameters are estimated with a particular kind of estimators. It is shown that the proposed estimators…
This article discusses nonconforming finite element methods for convex minimization problems and systematically derives dual mixed formulations. Duality relations lead to simple error estimates that avoid an explicit treatment of…
We propose a new approach to sequential testing which is an adaptive (on-line) extension of the (off-line) framework developed in [10]. It relies upon testing of pairs of hypotheses in the case where each hypothesis states that the vector…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
A robust minimax test for two composite hypotheses, which are determined by the neighborhoods of two nominal distributions with respect to a set of distances - called $\alpha-$divergence distances, is proposed. Sion's minimax theorem is…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the…
A popular approach for estimating an unknown signal from noisy, linear measurements is via solving a so called \emph{regularized M-estimator}, which minimizes a weighted combination of a convex loss function and of a convex (typically,…
In this work we consider optimal stopping problems with conditional convex risk measures called optimised certainty equivalents. Without assuming any kind of time-consistency for the underlying family of risk measures, we derive a novel…