Related papers: Sharp Empirical Bernstein Bounds for the Variance …
We present two sharp, closed-form empirical Bernstein inequalities for symmetric random matrices with bounded eigenvalues. By sharp, we mean that both inequalities adapt to the unknown variance in a tight manner: the deviation captured by…
Operator-valued concentration inequalities are foundational to the analysis of modern high-dimensional statistics and randomized algorithms. However, standard oracle bounds are frequently limited in practice: they require explicit a priori…
Concentration inequalities quantify the deviation of a random variable from a fixed value. In spite of numerous applications, such as opinion surveys or ecological counting procedures, few concentration results are known for the setting of…
We derive a new closed-form variance-adaptive confidence sequence (CS) for estimating the average conditional mean of a sequence of bounded random variables. Empirically, it yields the tightest closed-form CS we have found for tracking…
We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the…
We propose a consistent estimator of sharp bounds on the variance of the difference-in-means estimator in completely randomized experiments. Generalizing Robins [Stat. Med. 7 (1988) 773-785], our results resolve a well-known identification…
Learning from non-independent and non-identically distributed data poses a persistent challenge in statistical learning. In this study, we introduce data-dependent Bernstein inequalities tailored for vector-valued processes in Hilbert…
We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bounded random variables with exponential decay of the strong…
We establish nonuniform Berry-Esseen bounds for martingales under the conditional Bernstein condition. These bounds imply Cram\'er type large deviations for moderate $x$'s, and are of exponential decay rate as de la Pe\~na's inequality when…
Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.
We present some extensions of Bernstein's concentration inequality for random matrices. This inequality has become a useful and powerful tool for many problems in statistics, signal processing and theoretical computer science. The main…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
In this paper we derive sharp lower and upper bounds for the covariance of two bounded random variables when knowledge about their expected values, variances or both is available. When only the expected values are known, our result can be…
We establish some deviation inequalities, moment bounds and almost sure results for the Wasserstein distance of order p $\in$ [1, $\infty$) between the empirical measure of independent and identically distributed R d-valued random variables…
In this paper, we consider the nonasymptotic sequential estimation of means of random variables bounded in between zero and one. We have rigorously demonstrated that, in order to guarantee prescribed relative precision and confidence level,…
In a completely randomized experiment, the variances of treatment effect estimators in the finite population are usually not identifiable and hence not estimable. Although some estimable bounds of the variances have been established in the…
In this paper, we are concerned with obtaining distribution-free concentration inequalities for mixture of independent Bernoulli variables that incorporate a notion of variance. Missing mass is the total probability mass associated to the…
We present novel bounds for estimating discrete probability distributions under the $\ell_\infty$ norm. These are nearly optimal in various precise senses, including a kind of instance-optimality. Our data-dependent convergence guarantees…