Related papers: De-biasing convex regularized estimators and inter…

We provide novel theoretical results regarding local optima of regularized $M$-estimators, allowing for nonconvexity in both loss and penalty functions. Under restricted strong convexity on the loss and suitable regularity conditions on the…

This work proposes new estimators for discrete optimal transport plans that enjoy Gaussian limits centered at the true solution. This behavior stands in stark contrast with the performance of existing estimators, including those based on…

This paper develops asymptotic normality results for individual coordinates of robust M-estimators with convex penalty in high-dimensions, where the dimension $p$ is at most of the same order as the sample size $n$, i.e, $p/n\le\gamma$ for…

We study theoretical properties of regularized robust M-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and…

A generic out-of-sample error estimate is proposed for robust $M$-estimators regularized with a convex penalty in high-dimensional linear regression where $(X,y)$ is observed and $p,n$ are of the same order. If $\psi$ is the derivative of…

There are many settings where researchers are interested in estimating average treatment effects and are willing to rely on the unconfoundedness assumption, which requires that the treatment assignment be as good as random conditional on…

In high-dimensional regression, we attempt to estimate a parameter vector $\beta_0\in\mathbb{R}^p$ from $n\lesssim p$ observations $\{(y_i,x_i)\}_{i\leq n}$ where $x_i\in\mathbb{R}^p$ is a vector of predictors and $y_i$ is a response…

In this paper, we propose an abstract procedure for debiasing constrained or regularized potentially high-dimensional linear models. It is elementary to show that the proposed procedure can produce $\frac{1}{\sqrt{n}}$-confidence intervals…

Completely randomized experiment is the gold standard for causal inference. When the covariate information for each experimental candidate is available, one typical way is to include them in covariate adjustments for more accurate treatment…

When data is collected in an adaptive manner, even simple methods like ordinary least squares can exhibit non-normal asymptotic behavior. As an undesirable consequence, hypothesis tests and confidence intervals based on asymptotic normality…

This paper studies schemes to de-bias the Lasso in a linear model $y=X\beta+\epsilon$ where the goal is to construct confidence intervals for $a_0^T\beta$ in a direction $a_0$, where $X$ has iid $N(0,\Sigma)$ rows. We show that previously…

We consider the problem of learning a coefficient vector $x_{0}$ in $R^{N}$ from noisy linear observations $y=Fx_{0}+w$ in $R^{M}$ in the high dimensional limit $M,N$ to infinity with $\alpha=M/N$ fixed. We provide a rigorous derivation of…

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,…

In this paper, we are concerned with regularized regression problems where the prior regularizer is a proper lower semicontinuous and convex function which is also partly smooth relative to a Riemannian submanifold. This encompasses as…

Popular regularizers with non-differentiable penalties, such as Lasso, Elastic Net, Generalized Lasso, or SLOPE, reduce the dimension of the parameter space by inducing sparsity or clustering in the estimators' coordinates. In this paper,…

A common way to estimate an unknown convex regression function $f_0: \Omega \subset \mathbb{R}^d \rightarrow \mathbb{R}$ from a set of $n$ noisy observations is to fit a convex function that minimizes the sum of squared errors. However,…

This paper develops a convex approach for sparse one-dimensional deconvolution that improves upon L1-norm regularization, the standard convex approach. We propose a sparsity-inducing non-separable non-convex bivariate penalty function for…

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…

Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…

Location estimation is a central problem in functional data analysis. In this paper, we investigate penalized spline estimators of location for discretely sampled functional data under a broad class of convex loss functions. Our framework…