Related papers: Uniform Inference in High-Dimensional Threshold Re…

We propose a new probabilistic characterization of the uniform distribution on the hypersphere in terms of the distribution of pairwise inner products, extending the ideas of \citep{cuesta2009projection,cuesta2007sharp} in a data-driven…

The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…

Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…

In the statistical inference for long range dependent time series the shape of the limit distribution typically depends on unknown parameters. Therefore, we propose to use subsampling. We show the validity of subsampling for general…

Accurate statistical inference in logistic regression models remains a critical challenge when the ratio between the number of parameters and sample size is not negligible. This is because approximations based on either classical asymptotic…

We consider statistical inference in high-dimensional regression problems under affine constraints on the parameter space. The theoretical study of this is motivated by the study of genetic determinants of diseases, such as diabetes, using…

To estimate a sparse linear model from data with Gaussian noise, consilience from lasso and compressed sensing literatures is that thresholding estimators like lasso and the Dantzig selector have the ability in some situations to identify…

This paper develops new tools to quantify uncertainty in optimal decision making and to gain insight into which variables one should collect information about given the potential cost of measuring a large number of variables. We investigate…

Hypothesis tests in models whose dimension far exceeds the sample size can be formulated much like the classical studentized tests only after the initial bias of estimation is removed successfully. The theory of debiased estimators can be…

Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn…

We consider the problems of parameter estimation for several models of threshold ergodic diffusion processes in the asymptotics of large samples. These models are the direct continuous time analogues of the well-known in time series…

In various applications of regression analysis, in addition to errors in the dependent observations also errors in the predictor variables play a substantial role and need to be incorporated in the statistical modeling process. In this…

We study high-dimensional regression with missing entries in the covariates. A common strategy in practice is to \emph{impute} the missing entries with an appropriate substitute and then implement a standard statistical procedure acting as…

Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…

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…

We provide a selected overview of methodology and theory for estimation and inference on the edge weights in high-dimensional directed and undirected Gaussian graphical models. For undirected graphical models, two main explicit…

This paper studies the problem of statistical inference for genetic relatedness between binary traits based on individual-level genome-wide association data. Specifically, under the high-dimensional logistic regression models, we define…

Uncertainty estimation aims to evaluate the confidence of a trained deep neural network. However, existing uncertainty estimation approaches rely on low-dimensional distributional assumptions and thus suffer from the high dimensionality of…

We develop a unified $L$-statistic testing framework for high-dimensional regression coefficients that adapts to unknown sparsity. The proposed statistics rank coordinate-wise evidence measures and aggregate the top $k$ signals, bridging…

Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…