Related papers: High-dimensional regression with unknown variance

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 study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

Many high-dimensional data sets suffer from hidden confounding which affects both the predictors and the response of interest. In such situations, standard regression methods or algorithms lead to biased estimates. This paper substantially…

Censored data are quite common in statistics and have been studied in depth in the last years. In this paper we consider censored high-dimensional data. High-dimensional models are in some way more complex than their low-dimensional…

When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…

We devise a one-shot approach to distributed sparse regression in the high-dimensional setting. The key idea is to average "debiased" or "desparsified" lasso estimators. We show the approach converges at the same rate as the lasso as long…

We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…

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…

The Lasso is one of the most important approaches for parameter estimation and variable selection in high dimensional linear regression. At the heart of its success is the attractive rate of convergence result even when $p$, the dimension…

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…

Forward regression is a statistical model selection and estimation procedure which inductively selects covariates that add predictive power into a working statistical regression model. Once a model is selected, unknown regression parameters…

This paper is concerned with inference on the regression function of a high-dimensional linear model when outcomes are missing at random. We propose an estimator which combines a Lasso pilot estimate of the regression function with a bias…

Asymmetry along with heteroscedasticity or contamination often occurs with the growth of data dimensionality. In ultra-high dimensional data analysis, such irregular settings are usually overlooked for both theoretical and computational…

We consider the problem of sparse variable selection on high dimension heterogeneous data sets, which has been taking on renewed interest recently due to the growth of biological and medical data sets with complex, non-i.i.d. structures and…

Residual variance and the signal-to-noise ratio are important quantities in many statistical models and model fitting procedures. They play an important role in regression diagnostics, in determining the performance limits in estimation and…

We consider a high-dimensional regression model with a possible change-point due to a covariate threshold and develop the Lasso estimator of regression coefficients as well as the threshold parameter. Our Lasso estimator not only selects…

In this paper, we introduce ``UniLasso'' -- a novel statistical method for sparse regression. This two-stage approach preserves the signs of the univariate coefficients and leverages their magnitude. Both of these properties are attractive…

Recent studies in the literature have paid much attention to the sparsity in linear classification tasks. One motivation of imposing sparsity assumption on the linear discriminant direction is to rule out the noninformative features, making…

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…

For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised…