Related papers: Estimation of multiple mean vectors in high dimens…
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary…
Composite likelihood estimation has an important role in the analysis of multivariate data for which the full likelihood function is intractable. An important issue in composite likelihood inference is the choice of the weights associated…
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…
Asymmetry along with heteroscedasticity or contamination often occurs with the growth of data dimensionality. In ultra-high dimensional data analysis, such irregular settings are usually overlooked for both theoretical and computational…
We consider the problem of metric learning for multi-view data and present a novel method for learning within-view as well as between-view metrics in vector-valued kernel spaces, as a way to capture multi-modal structure of the data. We…
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…
A robust mean value is often a good alternative to the standard mean value when dealing with data containing many outliers. An efficient method for samples of one-dimensional features and the truncated quadratic error norm is presented and…
This article reviews recent progress in high-dimensional bootstrap. We first review high-dimensional central limit theorems for distributions of sample mean vectors over the rectangles, bootstrap consistency results in high dimensions, and…
In this work, we generalize the Cram\'er-von Mises statistic via projection-averaging to obtain a robust test for the multivariate two-sample problem. The proposed test is consistent against all fixed alternatives, robust to heavy-tailed…
It is well known that non-parametric methods suffer from the "curse of dimensionality". We propose here a new estimation method for a multivariate distribution, using sub-sampling and ranks, which seems not to suffer from this "curse". We…
This paper is about models for a vector of probabilities whose elements must have a multiplicative structure and sum to 1 at the same time; in certain applications, as basket analysis, these models may be seen as a constrained version of…
Multiple importance sampling (MIS) methods use a set of proposal distributions from which samples are drawn. Each sample is then assigned an importance weight that can be obtained according to different strategies. This work is motivated by…
Motivated by the likelihood ratio test under the Gaussian assumption, we develop a maximum sum-of-squares test for conducting hypothesis testing on high dimensional mean vector. The proposed test which incorporates the dependence among the…
Multivariate functions encountered in high-dimensional uncertainty quantification problems often vary most strongly along a few dominant directions in the input parameter space. We propose a gradient-based method for detecting these…
We study the asymptotic behavior of a class of methods for sufficient dimension reduction in high-dimension regressions, as the sample size and number of predictors grow in various alignments. It is demonstrated that these methods are…
We introduce a very general method for sparse and large-scale variable selection. The large-scale regression settings is such that both the number of parameters and the number of samples are extremely large. The proposed method is based on…
High-dimensional statistical inference with general estimating equations are challenging and remain less explored. In this paper, we study two problems in the area: confidence set estimation for multiple components of the model parameters,…
Based on two independent samples X_1,...,X_m and X_{m+1},...,X_n drawn from multivariate distributions with unknown Lebesgue densities p and q respectively, we propose an exact multiple test in order to identify simultaneously regions of…
In this paper we investigate the question of how much combined measurements can increase the accuracy of additive quantities. Therefore, we consider a set of measurements from a selection of all possible combinations of the $n$ labeled…
This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of…