Related papers: High-dimensional Data Bootstrap
Development of comprehensive prediction models are often of great interest in many disciplines of science, but datasets with information on all desired features often have small sample sizes. We describe a transfer learning approach for…
We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…
Most linear dimension reduction methods proposed in the literature can be formulated using an appropriate pair of scatter matrices, see e.g. Ye and Weiss (2003), Tyler et al. (2009), Bura and Yang (2011), Liski et al. (2014) and Luo and Li…
This paper gives a theoretical analysis of high dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis on the poor performances of standard procedures in the case when…
We obtain explicit error bounds for the $d$-dimensional normal approximation on hyperrectangles for a random vector that has a Stein kernel, or admits an exchangeable pair coupling, or is a non-linear statistic of independent random…
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…
An algorithm is described that enables efficient deterministic approximate computation of the bootstrap distribution for any linear bootstrap method $T_n^*$, alleviating the need for repeated resampling from observations (resp.…
Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…
This paper is devoted to the study of the general linear hypothesis testing (GLHT) problem of multi-sample high-dimensional mean vectors. For the GLHT problem, we introduce a test statistic based on $L^2$-norm and random integration method,…
In this paper, we propose a bootstrap method applied to massive data processed distributedly in a large number of machines. This new method is computationally efficient in that we bootstrap on the master machine without over-resampling,…
We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…
Most work on supervised learning research has focused on marginal predictions. In decision problems, joint predictive distributions are essential for good performance. Previous work has developed methods for assessing low-order predictive…
In this paper we study a bootstrap strategy for estimating the variance of a mean taken over large multifactor crossed random effects data sets. We apply bootstrap reweighting independently to the levels of each factor, giving each…
The recent seminal work of Chernozhukov, Chetverikov and Kato has shown that bootstrap approximation for the maximum of a sum of independent random vectors is justified even when the dimension is much larger than the sample size. In this…
The bootstrap provides a simple and powerful means of assessing the quality of estimators. However, in settings involving large datasets, the computation of bootstrap-based quantities can be prohibitively demanding. As an alternative, we…
The visualization of multi-dimensional data with interpretable methods remains limited by capabilities for both high-dimensional lossless visualizations that do not suffer from occlusion and that are computationally capable by parameterized…
Factor analysis is a widely used statistical tool in many scientific disciplines, such as psychology, economics, and sociology. As observations linked by networks become increasingly common, incorporating network structures into factor…
Let $X_1, \ldots, X_n\in\mathbb{R}^p$ be i.i.d. random vectors. We aim to perform simultaneous inference for the mean vector $\mathbb{E} (X_i)$ with finite polynomial moments and an ultra high dimension. Our approach is based on the…
Many statistical applications require the quantification of joint dependence among more than two random vectors. In this work, we generalize the notion of distance covariance to quantify joint dependence among d >= 2 random vectors. We…