Related papers: Pivotal Estimation via Self-Normalization for High…
We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The…
Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…
Several new estimation methods have been recently proposed for the linear regression model with observation error in the design. Different assumptions on the data generating process have motivated different estimators and analysis. In…
We consider the linear regression model with observation error in the design. In this setting, we allow the number of covariates to be much larger than the sample size. Several new estimation methods have been recently introduced for this…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…
This paper studies inference in the high-dimensional linear regression model with outliers. Sparsity constraints are imposed on the vector of coefficients of the covariates. The number of outliers can grow with the sample size while their…
We study estimation and testing in the Poisson regression model with noisy high dimensional covariates, which has wide applications in analyzing noisy big data. Correcting for the estimation bias due to the covariate noise leads to a…
This work addresses the issue of large covariance matrix estimation in high-dimensional statistical analysis. Recently, improved iterative algorithms with positive-definite guarantee have been developed. However, these algorithms cannot be…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…
The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…
Although a majority of the theoretical literature in high-dimensional statistics has focused on settings which involve fully-observed data, settings with missing values and corruptions are common in practice. We consider the problems of…
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model.…
In high dimensional sparse regression, pivotal estimators are estimators for which the optimal regularization parameter is independent of the noise level. The canonical pivotal estimator is the square-root Lasso, formulated along with its…
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…
We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant…
We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints ($\ell_q$ constraint with $0<q\leq1$) in the high-dimensional setting. We first present a…
The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…
Penalized estimation principle is fundamental to high-dimensional problems. In the literature, it has been extensively and successfully applied to various models with only structural parameters. As a contrast, in this paper, we apply this…
This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…