Related papers: Bounds on inequality with incomplete data
Human-generated categorical annotations frequently produce empirical response distributions (soft labels) that reflect ambiguity rather than simple annotator error. We introduce an ambiguity measure that maps a discrete response…
In this paper, we propose a branch-and-bound algorithm for solving nonconvex quadratic programming problems with box constraints (BoxQP). Our approach combines existing tools, such as semidefinite programming (SDP) bounds strengthened…
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…
In the first part of this study, a convex-constrained penalized formulation was studied for a class of constant modulus (CM) problems. In particular, the error bound techniques were shown to play a vital role in providing exact penalization…
We derive an inequality for the linear entropy, that gives sharp bounds for all finite dimensional systems. The derivation is based on generalised Bloch decompositions and provides a strict improvement for the possible distribution of…
To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-justified infinite-dimensional Bayesian analysis methods have…
Income inequality estimators are biased in small samples, leading generally to an underestimation. This aspect deserves particular attention when estimating inequality in small domains and performing small area estimation at the area level.…
Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…
A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis…
In many astronomical problems one often needs to determine the upper and/or lower boundary of a given data set. An automatic and objective approach consists in fitting the data using a generalised least-squares method, where the function to…
We consider the inverse boundary value problem of determining a coefficient function in an elliptic partial differential equation from knowledge of the associated Neumann-Dirichlet-operator. The unknown coefficient function is assumed to be…
This paper expands the notion of robust moment problems to incorporate distributional ambiguity using Wasserstein distance as the ambiguity measure. The classical Chebyshev-Cantelli (zeroth partial moment) inequalities, Scarf and Lo (first…
This paper establishes pointwise estimates up to boundary for the gradient of weak solutions to a class of very singular quasilinear elliptic equations with mixed data: \begin{cases} -\operatorname{div}(A(x,D u))=g-\operatorname{div} f…
We use novel integral representations developed by the second author to prove certain rigorous results concerning elliptic boundary value problems in convex polygons. Central to this approach is the so-called global relation, which is a…
Studies on simulation input uncertainty often built on the availability of input data. In this paper, we investigate an inverse problem where, given only the availability of output data, we nonparametrically calibrate the input models and…
We develop a unified framework for semilinear elliptic equations with gradient-dependent nonlinearities and singular weights in strictly convex domains. Considering large solutions of \[ -\Delta u + b(x)\,h(|\nabla u|) + a(x)\,u = f(x)…
Ratios of integrals can be bounded in terms of ratios of integrands under certain monotonicity conditions. This result, related with L'H\^{o}pital's monotone rule, can be used to obtain sharp bounds for cumulative distribution functions. We…
Many statistical estimands of interest (e.g., in regression or causality) are functions of the joint distribution of multiple random variables. But in some applications, data is not available that measures all random variables on each…
This note presents sharp inequalities for deviation probability of a general quadratic form of a random vector \(\xiv\) with finite exponential moments. The obtained deviation bounds are similar to the case of a Gaussian random vector. The…
In semivarying coefficient models for longitudinal/clustered data, usually of primary interest is usually the parametric component which involves unknown constant coefficients. First, we study semiparametric efficiency bound for estimation…