Related papers: Sharp bounds on the variance in randomized experim…

We present a new method for constructing a confidence interval for the mean of a bounded random variable from samples of the random variable. We conjecture that the confidence interval has guaranteed coverage, i.e., that it contains the…

Causal inference from observational data provides strong evidence for the best action in decision-making without performing expensive randomized trials. The effect of an action is usually not identifiable under unobserved confounding, even…

The paper suggests a simple method of deriving minimax lower bounds to the accuracy of statistical inference on heavy tails. A well-known result by Hall and Welsh (Ann. Statist. 12 (1984) 1079-1084) states that if $\hat{\alpha}_n$ is an…

Gau\ss (1823) proved a sharp upper bound on the probability that a random variable falls outside a symmetric interval around zero when its distribution is unimodal with mode at zero. For the class of all distributions with mean at zero,…

Many algorithms have been recently proposed for causal machine learning. Yet, there is little to no theory on their quality, especially considering finite samples. In this work, we propose a theory based on generalization bounds that…

We derive an (almost) guaranteed upper bound on the error of deep neural networks under distribution shift using unlabeled test data. Prior methods either give bounds that are vacuous in practice or give estimates that are accurate on…

We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…

We observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…

A novel way of defining limits in classical statistics is proposed. This is a natural extension of the original Neyman's method, and has the desirable property that only information relevant to the problem is used in making statistical…

Chebyshev's inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the…

We establish sharp large-deviation asymptotic estimates for the maximum order statistic of i.i.d.\ standard normal random variables on all Borel subsets of the positive real line. This result yields more accurate tail approximations than…

While attractive from a theoretical perspective, finely stratified experiments such as paired designs suffer from certain analytical limitations not present in block-randomized experiments with multiple treated and control individuals in…

Deriving generalization bounds for stable algorithms is a classical question in learning theory taking its roots in the early works by Vapnik and Chervonenkis (1974) and Rogers and Wagner (1978). In a series of recent breakthrough papers by…

Recent development in high-dimensional statistical inference has necessitated concentration inequalities for a broader range of random variables. We focus on sub-Weibull random variables, which extend sub-Gaussian or sub-exponential random…

For an ergodic Brownian diffusion with invariant measure $\nu$, we consider a sequence of empirical distributions ($\nu$n) n$\ge$1 associated with an approximation scheme with decreasing time step ($\gamma$n) n$\ge$1 along an adapted…

We construct and analyze an estimator of association between random variables based on their similarity in both direction and magnitude. Under special conditions, the proposed measure becomes a robust and consistent estimator of the linear…

In causal inference, treatment effects are typically estimated under the ignorability, or unconfoundedness, assumption, which is often unrealistic in observational data. By relaxing this assumption and conducting a sensitivity analysis, we…

We study distributionally robust optimization (DRO) problems with uncertainty sets consisting of high-dimensional random vectors that are close in the multivariate Wasserstein distance to a reference random vector. We give conditions when…

In randomized experiments, the actual treatments received by some experimental units may differ from their treatment assignments. This non-compliance issue often occurs in clinical trials, social experiments, and the applications of…

We study the problem of approximately recovering a probability distribution given noisy measurements of its Chebyshev polynomial moments. This problem arises broadly across algorithms, statistics, and machine learning. By leveraging a…