Related papers: Concentration of the bootstrap empirical process, …

Bootstrap smoothed (bagged) parameter estimators have been proposed as an improvement on estimators found after preliminary data-based model selection. The key result of Efron (2014) is a very convenient and widely applicable formula for a…

First-passage properties are central to the kinetics of target-search processes. Theoretical approaches so far primarily focused on predicting first-passage statistics for a given process or model. In practice, however, one faces the…

Exchangeable arrays are natural tools to model common forms of dependence between units of a sample. Jointly exchangeable arrays are well suited to dyadic data, where observed random variables are indexed by two units from the same…

Reliable uncertainty quantification remains a central challenge in predictive modeling. While Bayesian methods are theoretically appealing, their predictive intervals can exhibit poor frequentist calibration, particularly with small sample…

The bootstrap variance estimate is widely used in semiparametric inferences. However, its theoretical validity is a well known open problem. In this paper, we provide a {\em first} theoretical study on the bootstrap moment estimates in…

We propose new concentration inequalities for self-normalized martingales. The main idea is to introduce a suitable weighted sum of the predictable quadratic variation and the total quadratic variation of the martingale. It offers much more…

The consistency of a bootstrap or resampling scheme is classically validated by weak convergence of conditional laws. However, when working with stochastic processes in the space of bounded functions and their weak convergence in the…

The bootstrap is a method for estimating the distribution of an estimator or test statistic by re-sampling the data or a model estimated from the data. Under conditions that hold in a wide variety of econometric applications, the bootstrap…

We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution.…

We study the rate of convergence of the Mallows distance between the empirical distribution of a sample and the underlying population. The surprising feature of our results is that the convergence rate is slower in the discrete case than in…

We study batched bandit experiments and consider the problem of inference conditional on the realized stopping time, assignment probabilities, and target parameter, where all of these may be chosen adaptively using information up to the…

This note is concerned with weakly interacting stochastic particle systems with possibly singular pairwise interactions. In this setting, we observe a connection between entropic propagation of chaos and exponential concentration bounds for…

While researchers commonly use the bootstrap for statistical inference, many of us have realized that the standard bootstrap, in general, does not work for Chatterjee's rank correlation. In this paper, we provide proof of this issue under…

We give a concentration inequality based on the premise that random variables take values within a particular region. The concentration inequality guarantees that, for any sequence of correlated random variables, the difference between the…

In the extreme value analysis of time series, not only the tail behavior is of interest, but also the serial dependence plays a crucial role. Drees and Rootz\'en (2010) established limit theorems for a general class of empirical processes…

Choosing models from a hypothesis space is a frequent task in approximation theory and inverse problems. Cross-validation is a classical tool in the learner's repertoire to compare the goodness of fit for different reconstruction models.…

The validity of various bootstrapping methods has been proved for the sample mean of strongly mixing data. But in many applications, there appear nonlinear statistics of processes that are not strongly mixing. We investigate the…

This paper provides a bound for the supremum of sample averages over a class of functions for a general class of mixing stochastic processes with arbitrary mixing rates. Regardless of the speed of mixing, the bound is comprised of a…

This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…

Model averaging has gained significant attention in recent years due to its ability of fusing information from different models. The critical challenge in frequentist model averaging is the choice of weight vector. The bootstrap method,…