Related papers: Bootstrapping Max Statistics in High Dimensions: N…
In this paper we develop non-asymptotic Gaussian approximation results for the sampling distribution of suprema of empirical processes when the indexing function class $\mathcal{F}_n$ varies with the sample size $n$ and may not be Donsker.…
Many statistical methodologies for high-dimensional data assume the population is normal. Although a few multivariate normality tests have been proposed, to the best of our knowledge, none of them can properly control the type I error when…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
Scientific explanation often requires inferring maximally predictive features from a given data set. Unfortunately, the collection of minimal maximally predictive features for most stochastic processes is uncountably infinite. In such…
This paper concerns the approximation of smooth, high-dimensional functions from limited samples using polynomials. This task lies at the heart of many applications in computational science and engineering - notably, some of those arising…
Estimating some mathematical expectations from partially observed data and in particular missing outcomes is a central problem encountered in numerous fields such as transfer learning, counterfactual analysis or causal inference. Matching…
In this paper we address the problem of performing statistical inference for large scale data sets i.e., Big Data. The volume and dimensionality of the data may be so high that it cannot be processed or stored in a single computing node. We…
Multi-layer feedforward networks have been used to approximate a wide range of nonlinear functions. An important and fundamental problem is to understand the learnability of a network model through its statistical risk, or the expected…
We employ stabilization methods and second order Poincar\'e inequalities to establish rates of multivariate normal convergence for a large class of vectors $(H_s^{(1)},...,H_s^{(m)})$, $s \geq 1$, of statistics of marked Poisson processes…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
With the proliferation of modern high-resolution measuring instruments mounted on satellites, planes, ground-based vehicles and monitoring stations, a need has arisen for statistical methods suitable for the analysis of large spatial…
Recent years have witnessed much progress on Gaussian and bootstrap approximations to the distribution of sums of independent random vectors with dimension $d$ large relative to the sample size $n$. However, for any number of moments $m>2$…
For hypothesis testing of functional parameters, given a functional statistic $T_n$ and a functional depth $D$ with respect to the distribution $P_n$ of $T_n$, we propose the depth value $DT_n \equiv D(T_n;P_n)$ as a test statistic, which…
Diffusion models generate samples by estimating the score function of the target distribution at various noise levels. The model is trained using samples drawn from the target distribution by progressively adding noise. Previous sample…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
A multiplier bootstrap procedure for construction of likelihood-based confidence sets is considered for finite samples and a possible model misspecification. Theoretical results justify the bootstrap validity for a small or moderate sample…
The limiting distribution for M-estimates in a non-stationary autoregressive model with heavy-tailed error is computationally intractable. To make inferences based on the M-estimates, the bootstrap procedure can be used to approximate the…
Bootstrap for nonlinear statistics like U-statistics of dependent data has been studied by several authors. This is typically done by producing a bootstrap version of the sample and plugging it into the statistic. We suggest an alternative…
A core problem in statistical network analysis is to develop network analogues of classical techniques. The problem of bootstrapping network data stands out as especially challenging, since typically one observes only a single network,…