Related papers: Minimax-optimal nonparametric regression in high d…

We investigate the feature compression of high-dimensional ridge regression using the optimal subsampling technique. Specifically, based on the basic framework of random sampling algorithm on feature for ridge regression and the A-optimal…

In nonparametric regression problems involving multiple predictors, there is typically interest in estimating an anisotropic multivariate regression surface in the important predictors while discarding the unimportant ones. Our focus is on…

Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…

This paper explores the validity of the two-stage estimation procedure for sparse linear models in high-dimensional settings with possibly many endogenous regressors. In particular, the number of endogenous regressors in the main equation…

High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…

We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first…

Estimation and prediction problems for dense signals are often framed in terms of minimax problems over highly symmetric parameter spaces. In this paper, we study minimax problems over l2-balls for high-dimensional linear models with…

We study minimax rates for high-dimensional linear regression with additive errors under the $\ell_p\ (1\leq p<\infty)$-losses, where the regression parameter is of weak sparsity. Our lower and upper bounds agree up to constant factors,…

Transfer learning for nonparametric regression is considered. We first study the non-asymptotic minimax risk for this problem and develop a novel estimator called the confidence thresholding estimator, which is shown to achieve the minimax…

Many regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation schemes. We show that a simple non-negative or…

Given $m$ $d$-dimensional responsors and $n$ $d$-dimensional predictors, sparse regression finds at most $k$ predictors for each responsor for linear approximation, $1\leq k \leq d-1$. The key problem in sparse regression is subset…

We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…

We study the problem of estimating a multivariate convex function defined on a convex body in a regression setting with random design. We are interested in optimal rates of convergence under a squared global continuous $l_2$ loss in the…

There is increasing interest in the problem of nonparametric regression with high-dimensional predictors. When the number of predictors $D$ is large, one encounters a daunting problem in attempting to estimate a $D$-dimensional surface…

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…

Sparse linear regression is one of the classical and extensively studied problems in high-dimensional statistics and compressed sensing. Despite the substantial body of literature dedicated to this problem, the precise determination of its…

Nonlinear regression analysis is a popular and important tool for scientists and engineers. In this article, we introduce theories and methods of nonlinear regression and its statistical inferences using the frequentist and Bayesian…

The choice of the tuning parameter in the Lasso is central to its statistical performance in high-dimensional linear regression. In this work, we study tuning regimes under which the Lasso exhibits suboptimal prediction performance, in the…

This paper proposes a multi-stage projection-based Lasso procedure for the semiparametric sample selection model in high-dimensional settings under a weak nonparametric restriction on the selection correction. In particular, the number of…

Linear regression without correspondences concerns the recovery of a signal in the linear regression setting, where the correspondences between the observations and the linear functionals are unknown. The associated maximum likelihood…