Related papers: High-Dimensional Inference Based on the Leave-One-…
Among the most popular variable selection procedures in high-dimensional regression, Lasso provides a solution path to rank the variables and determines a cut-off position on the path to select variables and estimate coefficients. In this…
Penalized regression models such as the Lasso have proved useful for variable selection in many fields - especially for situations with high-dimensional data where the numbers of predictors far exceeds the number of observations. These…
We propose a computationally intensive method, the random lasso method, for variable selection in linear models. The method consists of two major steps. In step 1, the lasso method is applied to many bootstrap samples, each using a set of…
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…
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…
Variable selection plays a fundamental role in high-dimensional data analysis. Various methods have been developed for variable selection in recent years. Well-known examples are forward stepwise regression (FSR) and least angle regression…
We propose a test of many zero parameter restrictions in a high dimensional linear iid regression model with $k$ $>>$ $n$ regressors. The test statistic is formed by estimating key parameters one at a time based on many low dimension…
In high-dimensions, many variable selection methods, such as the lasso, are often limited by excessive variability and rank deficiency of the sample covariance matrix. Covariance sparsity is a natural phenomenon in high-dimensional…
In the sparse linear regression setting, we consider testing the significance of the predictor variable that enters the current lasso model, in the sequence of models visited along the lasso solution path. We propose a simple test statistic…
In this paper, we develop invariance-based procedures for testing and inference in high-dimensional regression models. These procedures, also known as randomization tests, provide several important advantages. First, for the global null…
In recent years, there has been considerable theoretical development regarding variable selection consistency of penalized regression techniques, such as the lasso. However, there has been relatively little work on quantifying the…
Additive isotonic regression attempts to determine the relationship between a multi-dimensional observation variable and a response, under the constraint that the estimate is the additive sum of univariate component effects that are…
We propose a new testing procedure of heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. Our testing procedure is based on residuals of the Lasso. We demonstrate that…
It is more and more frequently the case in applications that the data we observe come from one or more random variables taking values in an infinite dimensional space, e.g. curves. The need to have tools adapted to the nature of these data…
In this paper, we propose a test procedure based on the LASSO methodology to test the global null hypothesis of no dependence between a response variable and $p$ predictors, where $n$ observations with $n < p$ are available. The proposed…
With now well-recognized non-negligible model selection uncertainty, data analysts should no longer be satisfied with the output of a single final model from a model selection process, regardless of its sophistication. To improve…
Sparse regression such as the Lasso has achieved great success in handling high-dimensional data. However, one of the biggest practical problems is that high-dimensional data often contain large amounts of missing values. Convex Conditioned…
Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…
Variable selection in high-dimensional scenarios is of great interested in statistics. One application involves identifying differentially expressed genes in genomic analysis. Existing methods for addressing this problem have some limits or…
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…