Related papers: Bootstrap in High Dimension with Low Computation
Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…
Although much progress has been made in the theory and application of bootstrap approximations for max statistics in high dimensions, the literature has largely been restricted to cases involving light-tailed data. To address this issue, we…
Approximate Bayesian computation (ABC) is computationally intensive for complex model simulators. To exploit expensive simulations, data-resampling via bootstrapping can be employed to obtain many artificial datasets at little cost.…
In statistical exercises where there are several candidate models, the traditional approach is to select one model using some data driven criterion and use that model for estimation, testing and other purposes, ignoring the variability of…
This paper studies the Gaussian and bootstrap approximations for the probabilities of a non-degenerate U-statistic belonging to the hyperrectangles in $\mathbb{R}^d$ when the dimension $d$ is large. A two-step Gaussian approximation…
A/B testing, a widely used form of Randomized Controlled Trial (RCT), is a fundamental tool in business data analysis and experimental design. However, despite its intent to maintain randomness, A/B testing often faces challenges that…
Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…
We develop theoretical finite-sample results concerning the size of wild bootstrap-based heteroskedasticity robust tests in linear regression models. In particular, these results provide an efficient diagnostic check, which can be used to…
Residual bootstrap is a classical method for statistical inference in regression settings. With massive data sets becoming increasingly common, there is a demand for computationally efficient alternatives to residual bootstrap. We propose a…
The process comparing the empirical cumulative distribution function of the sample with a parametric estimate of the cumulative distribution function is known as the empirical process with estimated parameters and has been extensively…
We characterize the statistical bootstrap for the estimation of information-theoretic quantities from data, with particular reference to its use in the study of large-scale social phenomena. Our methods allow one to preserve, approximately,…
Despite the performance advantages of modern sampling-based motion planners, solving high dimensional planning problems in near real-time remains a challenge. Applications include hyper-redundant manipulators, snake-like and humanoid…
This technical note presents a new approach to carrying out the kind of exploration achieved by Thompson sampling, but without explicitly maintaining or sampling from posterior distributions. The approach is based on a bootstrap technique…
In this paper, we propose a new statistical inference method for massive data sets, which is very simple and efficient by combining divide-and-conquer method and empirical likelihood. Compared with two popular methods (the bag of little…
Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…
In distributed, or privacy-preserving learning, we are often given a set of probabilistic models estimated from different local repositories, and asked to combine them into a single model that gives efficient statistical estimation. A…
A weighted regression procedure is proposed for regression type problems where the innovations are heavy-tailed. This method approximates the least absolute regression method in large samples, and the main advantage will be if the sample is…
Accurate uncertainty estimates can significantly improve the performance of iterative design of experiments, as in Sequential and Reinforcement learning. For many such problems in engineering and the physical sciences, the design task…
We provide new theoretical results in the field of inverse regression methods for dimension reduction. Our approach is based on the study of some empirical processes that lie close to a certain dimension reduction subspace, called the…
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a…