相关论文: Variable-width confidence intervals in Gaussian re…
We study the problem of robust linear regression with response variable corruptions. We consider the oblivious adversary model, where the adversary corrupts a fraction of the responses in complete ignorance of the data. We provide a nearly…
High-dimensional learning problems, where the number of features exceeds the sample size, often require sparse regularization for effective prediction and variable selection. While established for fully supervised data, these techniques…
We study confidence interval construction for linear regression under Huber's contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood,…
We address functional uncertainty quantification for ill-posed inverse problems where it is possible to evaluate a possibly rank-deficient forward model, the observation noise distribution is known, and there are known parameter…
We consider unbiased estimation of a sparse nonrandom vector corrupted by additive white Gaussian noise. We show that while there are infinitely many unbiased estimators for this problem, none of them has uniformly minimum variance.…
Beta regression is commonly employed when the outcome variable is a proportion. Since its conception, the approach has been widely used in applications spanning various scientific fields. A series of extensions have been proposed over time,…
A current strand of research in high-dimensional statistics deals with robustifying the available methodology with respect to deviations from the pervasive light-tail assumptions. In this paper we consider a linear mean regression model…
We compute bias, variance, and approximate confidence intervals for the efficiency of a random selection process under various special conditions that occur in practical data analysis. We consider the following cases: a) the number of…
We develop uniformly valid confidence regions for regression coefficients in a high-dimensional sparse median regression model with homoscedastic errors. Our methods are based on a moment equation that is immunized against non-regular…
We focus on the high dimensional linear regression $Y\sim\mathcal{N}(X\beta^{*},\sigma^{2}I_{n})$, where $\beta^{*}\in\mathds{R}^{p}$ is the parameter of interest. In this setting, several estimators such as the LASSO and the Dantzig…
Recently, high dimensional vector auto-regressive models (VAR), have attracted a lot of interest, due to novel applications in the health, engineering and social sciences. The presence of temporal dependence poses additional challenges to…
Crucial for building trust in deep learning models for critical real-world applications is efficient and theoretically sound uncertainty quantification, a task that continues to be challenging. Useful uncertainty information is expected to…
Among semiparametric regression models, partially linear additive models provide a useful tool to include additive nonparametric components as well as a parametric component, when explaining the relationship between the response and a set…
Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
We provide adaptive confidence intervals on a parameter of interest in the presence of nuisance parameters when some of the nuisance parameters have known signs. The confidence intervals are adaptive in the sense that they tend to be short…
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…
In this article the package High-dimensional Metrics (\texttt{hdm}) is introduced. It is a collection of statistical methods for estimation and quantification of uncertainty in high-dimensional approximately sparse models. It focuses on…
We propose a method for constructing confidence intervals that account for many forms of spatial correlation. The interval has the familiar `estimator plus and minus a standard error times a critical value' form, but we propose new methods…
An empirical Bayes confidence interval has high user demand in many applications. In particular, the second-order empirical Bayes confidence interval, the coverage error of which is of the third order for large number of areas, is widely…