Related papers: On Conditional Chisini Means and Risk Measures
Measuring and managing risk has become crucial in modern decision making under stochastic uncertainty. In two-stage stochastic programming, mean risk models are essentially defined by a parametric recourse problem and a quantification of…
Distributionally robust optimization involves various probability measures in its problem formulation. They can be bundled to constitute a risk functional. For this equivalence, risk functionals constitute a fundamental building block in…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
Elicitability is a property of $\mathbb{R}^k$-valued functionals defined on a set of distribution functions. These functionals represent statistical properties of a distribution, for instance its mean, variance, or median. They are called…
Simulation methods are among the most ubiquitous methodological tools in statistical science. In particular, statisticians often is simulation to explore properties of statistical functionals in models for which developed statistical theory…
We show the existence of nontrivial solutions for a class of highly quasilinear problems in which the governing operators depend on the unknown function. By using a suitable variational setting and a weak version of the Cerami-Palais-Smale…
This thesis presents the Conditional Value-at-Risk concept and combines an analysis that covers its application as a risk measure and as a vector norm. For both areas of application the theory is revised in detail and examples are given to…
The purpose of this paper is to discuss empirical risk minimization when the losses are not necessarily bounded and may have a distribution with heavy tails. In such situations, usual empirical averages may fail to provide reliable…
It is rigorously proved that quasilinear impulsive systems possess unpredictable solutions when a perturbation generated by an unpredictable sequence is applied. The existence, uniqueness, as well as asymptotic stability of such solutions…
We provide a constructive way of defining new elicitable risk measures that are characterised by a multiplicative scoring function. We show that depending on the choice of the scoring function's components, the resulting risk measure…
Mendelian randomization (MR) is widely used to uncover causal relationships in the presence of unmeasured confounders. However, most existing MR methods presuppose linear causality, risking bias when the true relationships are nonlinear,…
Let $(X,{\mathcal A},\mu)$ be a probability space and let $S\colon X\to X$ be a measurable transformation. Motivated by the paper of K. Nikodem [Czechoslovak Math. J. 41(116) (4) (1991) 565--569], we concentrate on a functional equation…
We show that a wide class of risk-constrained nonconvex functional optimization problems exhibit strong duality, regardless of nonconvexity. We develop two novel results under distinct sets of assumptions, establishing strong duality over…
In this paper we study a family of nonlinear (conditional) expectations that can be understood as a continuous semimartingale with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued…
Higher-order spectra (or polyspectra), defined as the Fourier Transform of a stationary process' autocumulants, are useful in the analysis of nonlinear and non Gaussian processes. Polyspectral means are weighted averages over Fourier…
We introduce a new regression method that relates the mean of an outcome variable to covariates, under the "adverse condition" that a distress variable falls in its tail. This allows to tailor classical mean regressions to adverse…
This paper considers the problem of testing whether there exists a solution satisfying certain non-negativity constraints to a linear system of equations. Importantly and in contrast to some prior work, we allow all parameters in the system…
We construct measure which determines a two-variable mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also…
An effective two-stage method for an estimation of parameters of the linear regression is considered. For this purpose we introduce a certain quasi-estimator that, in contrast to usual estimator, produces two alternative estimates. It is…
A symbolic method for solving linear recurrences of combinatorial and statistical interest is introduced. This method essentially relies on a representation of polynomial sequences as moments of a symbol that looks as the framework of a…