Related papers: Inequalities and bounds for expected order statist…

Developing classification methods with high accuracy that also avoid unfair treatment of different groups has become increasingly important for data-driven decision making in social applications. Many existing methods enforce fairness…

In this paper some new characterizing theorems of exponential distribution based on order statistics are presented. Some existing results are generalized and the open conjecture by Arnold and Villasenor is solved.

Measuring the concentration of random variables is a fundamental concept in probability and statistics. Here, we explore a type of concentration measure for continuous random variables with bounded support and use it to provide a notion of…

Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple…

``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are independent and identically distributed…

We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…

In probability theory and statistics, the IID model represents a single population, and a large, potentially infinite sample from this population. Main theorems, in particular the central limit theorem and laws of large number (LLN) assure…

Eliciting preferences from human judgements is inherently imprecise, yet most decision analysis methods force a single priority vector from pairwise comparisons, discarding the information embedded in inconsistencies. We instead leverage…

This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to…

Jensen's inequality, attributed to Johan Jensen -- a Danish mathematician and engineer noted for his contributions to the theory of functions -- is a ubiquitous result in convex analysis, providing a fundamental lower bound for the…

We propose new ways to compare two latent distributions when only ordinal data are available and without imposing parametric assumptions on the underlying continuous distributions. First, we contribute identification results. We show how…

Convex analysis is fundamental to proving inequalities that have a wide variety of applications in economics and mathematics. In this paper we provide Jensen-type inequalities for functions that are, intuitively, "very" convex. These…

Limit distributions for the greatest convex minorant and its derivative are considered for a general class of stochastic processes including partial sum processes and empirical processes, for independent, weakly dependent and long range…

Bayesian model averaging, obtained as the expectation of a likelihood function by a posterior distribution, has been widely used for prediction, evaluation of uncertainty, and model selection. Various approaches have been developed to…

We introduce a sieve for counting twin primes up to a given range. Our method depends on a parameter ${\lambda}_x$ and the estimation of the number of twin primes obtained as a result, is called a fundamental structure of the distribution…

Statistical estimation in many contemporary settings involves the acquisition, analysis, and aggregation of datasets from multiple sources, which can have significant differences in character and in value. Due to these variations, the…

A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory provides a law of large numbers: If the group satisfies…

Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…

Bounds on the log partition function are important in a variety of contexts, including approximate inference, model fitting, decision theory, and large deviations analysis. We introduce a new class of upper bounds on the log partition…

We propose a general analytical framework for single-facility continuous location problems under spatial demand uncertainty. In contrast to classical formulations based on discrete or regionally aggregated demands, the proposed model…