Related papers: High-dimensional regression with potential prior i…
In this paper, we apply shrinkage strategies to estimate regression coefficients efficiently for the high-dimensional multiple regression model, where the number of samples is smaller than the number of predictors. We assume in the sparse…
We address the challenge of correlated predictors in high-dimensional GLMs, where regression coefficients range from sparse to dense, by proposing a data-driven random projection method. This is particularly relevant for applications where…
In many important statistical analyses, the number of covariates $p$ often exceeds the data size $n$, a regime commonly referred to as high-dimensional. While considerable progress has been made in high-dimensional regression under the…
The least absolute shrinkage and selection operator (Lasso) is a popular method for high-dimensional statistics. However, it is known that the Lasso often has estimation bias and prediction error. To address such disadvantages, many…
We consider the problem of robustifying high-dimensional structured estimation. Robust techniques are key in real-world applications which often involve outliers and data corruption. We focus on trimmed versions of structurally regularized…
High-dimensional linear regression has been thoroughly studied in the context of independent and identically distributed data. We propose to investigate high-dimensional regression models for independent but non-identically distributed…
This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors…
Fitting linear regression models can be computationally very expensive in large-scale data analysis tasks if the sample size and the number of variables are very large. Random projections are extensively used as a dimension reduction tool…
We study high-dimensional regression with missing entries in the covariates. A common strategy in practice is to \emph{impute} the missing entries with an appropriate substitute and then implement a standard statistical procedure acting as…
Lasso-type estimators are routinely used to estimate high-dimensional time series models. The theoretical guarantees established for these estimators typically require the penalty level to be chosen in a suitable fashion often depending on…
We study the problem of high-dimensional regression when there may be interacting variables. Approaches using sparsity-inducing penalty functions such as the Lasso can be useful for producing interpretable models. However, when the number…
In this work we propose a framework for constructing goodness of fit tests in both low and high-dimensional linear models. We advocate applying regression methods to the scaled residuals following either an ordinary least squares or Lasso…
We study regression discontinuity designs in which many predetermined covariates, possibly much more than the number of observations, can be used to increase the precision of treatment effect estimates. We consider a two-step estimator…
Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…
We consider the problem of model selection and estimation in sparse high dimensional linear regression models with strongly correlated variables. First, we study the theoretical properties of the dual Lasso solution, and we show that joint…
High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by…
Variable selection in ultrahigh-dimensional linear regression is challenging due to its high computational cost. Therefore, a screening step is usually conducted before variable selection to significantly reduce the dimension. Here we…
We propose a new measure of variable importance in high-dimensional regression based on the change in the LASSO solution path when one covariate is left out. The proposed procedure provides a novel way to calculate variable importance and…
Including a large number of predictors in the imputation model underlying a multiple imputation (MI) procedure is one of the most challenging tasks imputers face. A variety of high-dimensional MI techniques can help, but there has been…
Inference for high-dimensional logistic regression models using penalized methods has been a challenging research problem. As an illustration, a major difficulty is the significant bias of the Lasso estimator, which limits its direct…