Related papers: Inequalities for independent random vectors under …

We provide an elementary proof of the dual representation of Expected Shortfall on the space of integrable random variables over a general probability space. Unlike the results in the extant literature, our proof only exploits basic…

For some estimations and predictions, we solve minimization problems with asymmetric loss functions. Usually, we estimate the coefficient of regression for these problems. In this paper, we do not make such the estimation, but rather give a…

Uncertainty is ubiquitous in real-world data, and the assumptions underlying classical linear regression models are often violated in practice. Inspired by the theory of sublinear expectation, we consider a linear regression model where the…

We prove the following exponential inequality: Let $n\geq 1$ and let $X_1,...,X_n$ be $n$ independent identically distributed symmetric real-valued random variables. For any $x,y>0$, we have \[\mathbb{P}\big({X_1+...+X_n}\geq x,\,…

In this paper, we have established a new framework of truncated inverse sampling for estimating mean values of non-negative random variables such as binomial, Poisson, hyper-geometrical, and bounded variables. We have derived explicit…

We show that many well-known transforms in convex geometry (in particular, centroid body, convex floating body, and Ulam floating body) are special instances of a general construction, relying on applying sublinear expectations to random…

In this paper, we obtain some inequalities by using a kernel and an inequality which is a result of Young inequality. Besides we give some applications to special means.

If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…

We obtain variance inequalities for quadratic forms of weakly dependent random variables with bounded fourth moments. We also discuss two application. Namely, we use these inequalities for deriving the limiting spectral distribution of a…

Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across…

In this paper we prove some exponential inequalities involving the sinc function. We analyze and prove inequalities with constant exponents as well as inequalities with certain polynomial exponents. Also, we establish intervals in which…

We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. The standard…

In this note, we derive concentration inequalities for random vectors with subGaussian norm (a generalization of both subGaussian random vectors and norm bounded random vectors), which are tight up to logarithmic factors.

We propose a method for variable selection in multiple regression with random predictors. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating suitable permutation and…

This paper tackles the challenge of detecting unreliable behavior in regression algorithms, which may arise from intrinsic variability (e.g., aleatoric uncertainty) or modeling errors (e.g., model uncertainty). First, we formally introduce…

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

Given an imprecise probabilistic model over a continuous space, computing lower/upper expectations is often computationally hard to achieve, even in simple cases. Because expectations are essential in decision making and risk analysis,…

Accurately measuring discrimination is crucial to faithfully assessing fairness of trained machine learning (ML) models. Any bias in measuring discrimination leads to either amplification or underestimation of the existing disparity.…

We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.

The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably…