Related papers: On the representation of weakly maxitive monetary …
We study a general risk measure called the generalized shortfall risk measure, which was first introduced in Mao and Cai (2018). It is proposed under the rank-dependent expected utility framework, or equivalently induced from the cumulative…
In this paper, we explore several Fatou-type properties of risk measures. The paper continues to reveal that the strong Fatou property, which was introduced in [17], seems to be most suitable to ensure nice dual representations of risk…
The main objective of this paper is to look from the unique point of view at some phenomena arising in different areas of probability theory and mathematical statistics. We will try to understand what is common between classical…
The article is devoted to the estimation of the rate of convergence of integral functionals of a Markov process. Under the assumption that the given Markov process admits a transition probability density which is differentiable in $t$ and…
The optimal value function is one of the basic objects in the field of mathematical optimization, as it allows the evaluation of the variations in the cost/revenue generated while minimizing/maximizing a given function under some…
In this article, we prove a joint large deviation principle in $n$ for the \emph{empirical pair measure} and \emph{ empirical offspring measure} of critical multitype Galton-Watson trees conditioned to have exactly $n$ vertices in the weak…
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…
Important problems in causal inference, economics, and, more generally, robust machine learning can be expressed as conditional moment restrictions, but estimation becomes challenging as it requires solving a continuum of unconditional…
We demonstrate that the negative volume of any $s$-paramatrized quasiprobability, including the Glauber-Sudashan $P$-function, can be consistently defined and forms a continuous hierarchy of nonclassicality measures that are linear optical…
We prove weak convergence in a separable Hilbert space for estimators of high-dimensional regression coefficients, which yields asymptotic normality and enables direct use of standard asymptotic tools such as the continuous mapping theorem.…
We study a minimax risk of estimating inverse functions on a plane, while keeping an estimator is also invertible. Learning invertibility from data and exploiting an invertible estimator are used in many domains, such as statistics,…
In this paper, we develop the lower and upper bounds of worst-case distortion riskmetrics and weighted entropy for unimodal, and symmetric unimodal distributions when mean and variance information are available. We also consider the sharp…
We introduce the post-processing preorder and equivalence relations for general measurements on a possibly infinite-dimensional general probabilistic theory described by an order unit Banach space $E$ with a Banach predual. We define the…
The present paper introduces a theoretical framework through which the degree of risk aversion with respect to uncertain prices can be measured through the context of the indirect utility function (IUF) using a lab experiment. First, the…
Volatility, as a primary indicator of financial risk, forms the foundation of classical frameworks such as Markowitz's Portfolio Theory and the Efficient Market Hypothesis (EMH). However, its conventional use rests on assumptions-most…
In measure theory several results are known how measure spaces are transformed into each other. But since moment functionals are represented by a measure we investigate in this study the effects and implications of these measure…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
Many results have been proved for various nuclear norm penalized estimators of the uniform sampling matrix completion problem. However, most of these estimators are not robust: in most of the cases the quadratic loss function and its…
The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…
Let $\mu$ be a probability measure on $\mathbb{R}$. We give conditions on the Fourier transform of its density for functionals of the form $H(a)=\int_{\mathbb{R}^n}h(\langle a,x\rangle)\mu^n(dx)$ to be Schur monotone. As applications, we…