Related papers: Universal Bootstrap for Spectral Statistics: Beyon…
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…
The problem of constructing a simultaneous confidence surface for the 2-dimensional mean function of a non-stationary functional time series is challenging as these bands can not be built on classical limit theory for the maximum absolute…
The wild bootstrap is a popular resampling method in the context of time-to-event data analyses. Previous works established the large sample properties of it for applications to different estimators and test statistics. It can be used to…
We investigate properties of a bootstrap-based methodology for testing hypotheses about equality of certain characteristics of the distributions between different populations in the context of functional data. The suggested testing…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a…
We study the problem of distributional approximations to high-dimensional non-degenerate $U$-statistics with random kernels of diverging orders. Infinite-order $U$-statistics (IOUS) are a useful tool for constructing simultaneous prediction…
For more than $50$ years the {\it Mean Measure of Divergence} (MMD) has been one of the most prominent tools used in anthropology for the study of non-metric traits. However, one of the problems, in anthropology including palaeoanthropology…
In high-dimensional time series analysis, Gaussian approximation (GA) schemes under various distance measures or on various collections of subsets of the Euclidean space play a fundamental role in a wide range of statistical inference…
Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…
The block bootstrap approximates sampling distributions from dependent data by resampling data blocks. A fundamental problem is establishing its consistency for the distribution of a sample mean, as a prototypical statistic. We use a…
Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators.…
Standard statistical methods that do not take proper account of the complexity of survey design can lead to erroneous inferences when applied to survey data due to unequal selection probabilities, clustering, and other design features. In…
Under certain conditions, the largest eigenvalue of a sample covariance matrix undergoes a well-known phase transition when the sample size $n$ and data dimension $p$ diverge proportionally. In the subcritical regime, this eigenvalue has…
Riemannian Gaussian distributions were initially introduced as basic building blocks for learning models which aim to capture the intrinsic structure of statistical populations of positive-definite matrices (here called covariance…
We give a constructive proof for the superbosonization formula for invariant random matrix ensembles, which is the supersymmetry analog of the theory of Wishart matrices. Formulas are given for unitary, orthogonal and symplectic symmetry,…
We consider the problem of quantifying uncertainty for the estimation error of the leading eigenvector from Oja's algorithm for streaming principal component analysis, where the data are generated IID from some unknown distribution. By…
Recently, Tibshirani et al. (2016) proposed a method for making inferences about parameters defined by model selection, in a typical regression setting with normally distributed errors. Here, we study the large sample properties of this…
In modern experimental science, there is a common problem of estimating the coefficients of a linear regression in a context where the variables of interest cannot be observed simultaneously. When there is a categorical variable that is…
Randomized experiments are the gold standard for estimating treatment effects, and randomization serves as a reasoned basis for inference. In widely used stratified randomized experiments, randomization-based finite-population asymptotic…