Related papers: Confidence regions for high-dimensional generalize…

This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its…

In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…

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.…

Eliminating the effect of confounding in observational studies typically involves fitting a model for an outcome adjusted for covariates. When, as often, these covariates are high-dimensional, this necessitates the use of sparse estimators…

To successfully work on variable selection, sparse model structure has become a basic assumption for all existing methods. However, this assumption is questionable as it is hard to hold in most of cases and none of existing methods may…

We study a high-dimensional regression model. Aim is to construct a confidence set for a given group of regression coefficients, treating all other regression coefficients as nuisance parameters. We apply a one-step procedure with the…

Small area estimators that ignore the sampling design lack design consistency when the sampling mechanism is complex and may be severely biased under informative designs. Existing procedures that account for the survey weights under…

Suppose that we observe $y \in \mathbb{R}^f$ and $X \in \mathbb{R}^{f \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 \beta^* + \epsilon \\ X & = & X_0 + W \end{eqnarray*} where $X_0$ is a $f \times m$…

We consider high dimensional sparse regression, and develop strategies able to deal with arbitrary -- possibly, severe or coordinated -- errors in the covariance matrix $X$. These may come from corrupted data, persistent experimental…

Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…

This paper proposes a new method for estimating high-dimensional binary choice models. We consider a semiparametric model that places no distributional assumptions on the error term, allows for heteroskedastic errors, and permits endogenous…

Incorporating sparsity priors in learning tasks can give rise to simple, and interpretable models for complex high dimensional data. Sparse models have found widespread use in structure discovery, recovering data from corruptions, and a…

We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data,…

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 robust linear regression in high-dimension, when both the dimension $d$ and the number of data points $n$ diverge with a fixed ratio $\alpha=n/d$, and study a data model that includes outliers. We provide exact asymptotics for the…

We consider a general model for high-dimensional empirical risk minimization whereby the data $\mathbf{x}_i$ are $d$-dimensional Gaussian vectors, the model is parametrized by $\mathbf{\Theta}\in\mathbb{R}^{d\times k}$, and the loss depends…

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…

Models with dimension more than the available sample size are now commonly used in various applications. A sensible inference is possible using a lower-dimensional structure. In regression problems with a large number of predictors, the…

This paper proposes a bootstrap-assisted procedure to conduct simultaneous inference for high dimensional sparse linear models based on the recent de-sparsifying Lasso estimator (van de Geer et al. 2014). Our procedure allows the dimension…

In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive point estimation, the…