Related papers: Implementable confidence sets in high dimensional …
We consider high dimensional $M$-estimation in settings where the response $Y$ is possibly missing at random and the covariates $\mathbf{X} \in \mathbb{R}^p$ can be high dimensional compared to the sample size $n$. The parameter of interest…
A robust and sparse estimator for multinomial regression is proposed for high dimensional data. Robustness of the estimator is achieved by trimming the observations, and sparsity of the estimator is obtained by the elastic net penalty,…
In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained.…
Hard thresholding, LASSO , adaptive LASSO and SCAD point estimators have been suggested for use in the linear regression context when most of the components of the regression parameter vector are believed to be zero, a sparsity type of…
We consider the equivalent problems of estimating the residual variance, the proportion of explained variance $\eta$ and the signal strength in a high-dimensional linear regression model with Gaussian random design. Our aim is to understand…
High dimensional hypothesis test deals with models in which the number of parameters is significantly larger than the sample size. Existing literature develops a variety of individual tests. Some of them are sensitive to the dense and small…
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…
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…
Penalized (or regularized) regression, as represented by Lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of…
While conformal predictors reap the benefits of rigorous statistical guarantees on their error frequency, the size of their corresponding prediction sets is critical to their practical utility. Unfortunately, there is currently a lack of…
Meta-analysis, the statistical analysis of results from separate studies, is a fundamental building block of science. But the assumptions of classical meta-analysis models are not satisfied whenever publication bias is present, which causes…
We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…
Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…
We consider the problem of robustly testing the norm of a high-dimensional sparse signal vector under two different observation models. In the first model, we are given $n$ i.i.d. samples from the distribution…
Given a sample from some unknown continuous density $f:\mathbb{R}\to\mathbb{R}$, we construct adaptive confidence bands that are honest for all densities in a "generic" subset of the union of $t$-H\"older balls, $0<t\le r$, where $r$ is a…
For high-dimensional inference problems, statisticians have a number of competing interests. On the one hand, procedures should provide accurate estimation, reliable structure learning, and valid uncertainty quantification. On the other…
This article considers inference in linear instrumental variables models with many regressors, all of which could be endogenous. We propose the STIV estimator. Identification robust confidence sets are derived by solving linear programs. We…
Statistical inference of the high-dimensional regression coefficients is challenging because the uncertainty introduced by the model selection procedure is hard to account for. A critical question remains unsettled; that is, is it possible…
Simultaneous variable selection and statistical inference is challenging in high-dimensional data analysis. Most existing post-selection inference methods require explicitly specified regression models, which are often linear, as well as…
This paper studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient…