相关论文: The Lasso error is bounded iff its active set size…

This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…

Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…

We consider the problem of estimating a low-dimensional parameter in high-dimensional linear regression. Constructing an approximately unbiased estimate of the parameter of interest is a crucial step towards performing statistical…

The Lasso is a computationally efficient regression regularization procedure that can produce sparse estimators when the number of predictors (p) is large. Oracle inequalities provide probability loss bounds for the Lasso estimator at a…

We propose a self-tuning $\sqrt{\mathrm {Lasso}}$ method that simultaneously resolves three important practical problems in high-dimensional regression analysis, namely it handles the unknown scale, heteroscedasticity and (drastic)…

Given data $y$ and $k$ covariates $x$ one problem in linear regression is to decide which in any of the covariates to include when regressing $y$ on the $x$. If $k$ is small it is possible to evaluate each subset of the $x$. If however $k$…

We develop results for the use of Lasso and Post-Lasso methods to form first-stage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, $p$. Our results apply even when $p$ is much…

In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…

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…

We consider the problem of learning a coefficient vector x_0\in R^N from noisy linear observation y=Ax_0+w \in R^n. In many contexts (ranging from model selection to image processing) it is desirable to construct a sparse estimator x'. In…

Despite a large and significant body of recent work focused on estimating the out-of-sample risk of regularized models in the high dimensional regime, a theoretical understanding of this problem for non-differentiable penalties such as…

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…

Regularized regression approaches such as the Lasso have been widely adopted for constructing sparse linear models in high-dimensional datasets. A complexity in fitting these models is the tuning of the parameters which control the level of…

For statistical inference on regression models with a diverging number of covariates, the existing literature typically makes sparsity assumptions on the inverse of the Fisher information matrix. Such assumptions, however, are often…

Standard high-dimensional regression methods assume that the underlying coefficient vector is sparse. This might not be true in some cases, in particular in presence of hidden, confounding variables. Such hidden confounding can be…

We consider linear random coefficient regression models, where the regressors are allowed to have a finite support. First, we investigate identifiability, and show that the means and the variances and covariances of the random coefficients…

We propose a test of the significance of a variable appearing on the Lasso path and use it in a procedure for selecting one of the models of the Lasso path, controlling the Family-Wise Error Rate. Our null hypothesis depends on a set A of…

Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…

We leverage recent advances in high-dimensional statistics to derive new L2 estimation upper bounds for Lasso and Group Lasso in high-dimensions. For Lasso, our bounds scale as $(k^*/n) \log(p/k^*)$---$n\times p$ is the size of the design…

We study the problem of out-of-sample risk estimation in the high dimensional regime where both the sample size $n$ and number of features $p$ are large, and $n/p$ can be less than one. Extensive empirical evidence confirms the accuracy of…