Related papers: Some stochastic inequalities for weighted sums
Large deviations for sums of i.i.d.\ random variables with stretched-exponential tails (also called Weibull or semi-exponential tails) have been well understood since the 60's, going back to Nagaev's seminal work. Many extensions in the…
In many applications, data cluster. Failing to take the cluster structure into consideration generally leads to underestimated variances of point estimators and inflated type I errors in hypothesis tests. Many circumstance-dependent…
We study concentration inequalities for structured weighted sums of random data, including (i) tensor inner products and (ii) sequential matrix sums. We are interested in tail bounds and concentration inequalities for those structured…
Let $A_\pm>0$, $\beta\in(0,1)$, and let $Z^{(\alpha)}$ be a strictly $\alpha$-stable L\'evy process with the jump measure $\nu(\mathrm{d} z)=(C_+\mathbb{I}_{(0,\infty)}(z)+ C_-\mathbb{I}_{(-\infty,0)}(z))|z|^{-1-\alpha}\,\mathrm{d} z$,…
Win statistics, including the win ratio, net benefit, and win odds, summarize treatment effects on hierarchical composite endpoints by sequentially comparing patient pairs on component outcomes ordered by clinical importance, proceeding to…
It is a basic property of the entropy in statistical physics that is concave as a function of energy. The analog of this in representation theory would be the concavity of the logarithm of the multiplicity of an irreducible representation…
This paper is devoted to establishing exponential bounds for the probabilities of deviation of a sample sum from its expectation, when the variables involved in the summation are obtained by sampling in a finite population according to a…
Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g. uninsurable labor…
We utilize a discrete version of the notion of degree of freedom to prove a sharp min-entropy-variance inequality for integer valued log-concave random variables. More specifically, we show that the geometric distribution minimizes the…
We consider two methods to establish log-Sobolev inequalities for the invariant measure of a diffusion process when its density is not explicit and the curvature is not positive everywhere. In the first approach, based on the Holley-Stroock…
Aim of this article is to prove the inequality $n \sum_{i=1}^{n} a_ib_i \leq \sum_{i=1}^{n} a_i \sum_{i=1}^n b_i$ when $a_i$ are $n$ increasing positive real numbers and $b_i$ are $n$ decreasing real numbers. We also prove generalizations…
One tuple of probability vectors is more informative than another tuple when there exists a single stochastic matrix transforming the probability vectors of the first tuple into the probability vectors of the other. This is called matrix…
We study statistics dependence of the probability distributions and the means of measured moments of conserved quantities, respectively. The required statistics of all interested moments and their products are estimated based on a simple…
Inverse probability weighting (IPW) methods are commonly used to analyze non-ignorable missing data under the assumption of a logistic model for the missingness probability. However, solving IPW equations numerically may involve…
Shape constraints yield flexible middle grounds between fully nonparametric and fully parametric approaches to modeling distributions of data. The specific assumption of log-concavity is motivated by applications across economics, survival…
In this paper, we investigate a stochastic Hardy-Littlewood-Sobolev inequality. Due to the stochastic nature of the inequality, the relation between the exponents of intgrability is modified. This modification can be understood as a…
Inference for models with recursively defined likelihoods is computationally demanding, limiting scalability to large datasets. We propose a stabilised weighted subsampling methodology for accelerated inference based on an unbiased…
The Contextuality-by-Default approach to determining and measuring the (non)contextuality of a system of random variables requires that every random variable in the system be represented by an equivalent set of dichotomous random variables.…
The concept of "stochastic precedence" between two real-valued random variables has often emerged in different applied frameworks. In this paper we consider a slightly more general, and completely natural, concept of stochastic precedence…
Variable selection in linear regression has been a central topic in statistical research for decades. Bayesian variable selection methods, which account for uncertainty in both the regression coefficients and the noise variance, have…