Related papers: Rate optimal multiple testing procedure in high-di…
This paper presents a survey on some recent advances for the type I error rate control in multiple testing methodology. We consider the problem of controlling the $k$-family-wise error rate (kFWER, probability to make $k$ false discoveries…
Effectively controlling the false discovery rate (FDR) in high-dimensional variable selection is a fundamental statistical problem that has garnered significant research interest. In this paper, we propose a novel, user-friendly, and…
We study the problem of exact support recovery for high-dimensional sparse linear regression under independent Gaussian design when the signals are weak, rare, and possibly heterogeneous. Under a suitable scaling of the sample size and…
It is quite common in modern research, for a researcher to test many hypotheses. The statistical (frequentist) hypothesis testing framework, does not scale with the number of hypotheses in the sense that naively performing many hypothesis…
Much effort has been done to control the "false discovery rate" (FDR) when $m$ hypotheses are tested simultaneously. The FDR is the expectation of the "false discovery proportion" $\text{FDP}=V/R$ given by the ratio of the number of false…
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…
The large bulk of work in multiple testing has focused on specifying procedures that control the false discovery rate (FDR), with relatively less attention being paid to the corresponding Type II error known as the false non-discovery rate…
This paper is a review of the popular Benjamini Hochberg Method and other related useful methods of Multiple Hypothesis testing. This is written with the purpose of serving a short but complete easy to understand review of the main article…
This paper studies the problem of high-dimensional multiple testing and sparse recovery from the perspective of sequential analysis. In this setting, the probability of error is a function of the dimension of the problem. A simple…
The knockoff-based multiple testing setup of Barber & Candes (2015) for variable selection in multiple regression where sample size is as large as the number of explanatory variables is considered. The method of Benjamini & Hochberg (1995)…
We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the…
Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However,…
The generalized linear models (GLM) have been widely used in practice to model non-Gaussian response variables. When the number of explanatory features is relatively large, scientific researchers are of interest to perform controlled…
Multiple testing has been a popular topic in statistical research. Although vast works have been done, controlling the false discoveries remains a challenging task when the corresponding test statistics are dependent. Various methods have…
Feature selection is a critical task in machine learning and statistics. However, existing feature selection methods either (i) rely on parametric methods such as linear or generalized linear models, (ii) lack theoretical false discovery…
Computational capability often falls short when confronted with massive data, posing a common challenge in establishing a statistical model or statistical inference method dealing with big data. While subsampling techniques have been…
Estimation of a high dimensional precision matrix is a critical problem to many areas of statistics including Gaussian graphical models and inference on high dimensional data. Working under the structural assumption of sparsity, we propose…
Multiple hypothesis testing often involves composite nulls, i.e., nulls that are associated with two or more distributions. In many cases, it is reasonable to assume that there is a prior distribution on the distributions despite it is…
We consider the high-dimensional discriminant analysis problem. For this problem, different methods have been proposed and justified by establishing exact convergence rates for the classification risk, as well as the l2 convergence results…
The paper considers the problem of identifying the sparse different components between two high dimensional means of column-wise dependent random vectors. We show that the dependence can be utilized to lower the identification boundary for…