Related papers: Variable-width confidence intervals in Gaussian re…
In assessing prediction accuracy of multivariable prediction models, optimism corrections are essential for preventing biased results. However, in most published papers of clinical prediction models, the point estimates of the prediction…
Sparse regression is frequently employed in diverse scientific settings as a feature selection method. A pervasive aspect of scientific data that hampers both feature selection and estimation is the presence of strong correlations between…
In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…
Consider a linear regression model. Fan and Li (2001) describe the smoothly clipped absolute deviation (SCAD) point estimator of the regression parameter vector. To gain insight into the properties of this estimator, they consider an…
We develop joint confidence regions for linear regression coefficients when the regressors and errors are jointly stationary and ergodic with unspecified serial dependence. The method applies random smoothing, using an independent auxiliary…
We consider linear random coefficient regression models, where the regressors are allowed to have a finite support. First, we investigate identifiability, and show that the means and the variances and covariances of the random coefficients…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
Weighting methods are popular tools for estimating causal effects; assessing their robustness under unobserved confounding is important in practice. In the following paper, we introduce a new set of sensitivity models called "variance-based…
For regression model selection via maximum likelihood estimation, we adopt a vector representation of candidate models and study the likelihood ratio confidence region for the regression parameter vector of a full model. We show that when…
We propose a new estimator, the thresholded scaled Lasso, in high dimensional threshold regressions. First, we establish an upper bound on the $\ell_\infty$ estimation error of the scaled Lasso estimator of Lee et al. (2012). This is a…
We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…
This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for…
We consider a discrete time stochastic model with infinite variance and study the mean estimation problem as in Wang and Ramdas (2023). We refine the Catoni-type confidence sequence (abbr. CS) and use an idea of Bhatt et al. (2022) to…
This manuscript studies a general approach to construct confidence sets for the solution of stochastic optimization, rendering empirical risk minimization as special cases. Statistical inference for stochastic optimization poses significant…
Constructing confidence intervals for the coefficients of high-dimensional sparse linear models remains a challenge, mainly because of the complicated limiting distributions of the widely used estimators, such as the lasso. Several methods…
In the analysis of survey data it is of interest to estimate and quantify uncertainty about means or totals for each of several non-overlapping subpopulations, or areas. When the sample size for a given area is small, standard confidence…
Meinshausen and Buhlmann [Ann. Statist. 34 (2006) 1436--1462] showed that, for neighborhood selection in Gaussian graphical models, under a neighborhood stability condition, the LASSO is consistent, even when the number of variables is of…
We study the estimation capacity of the generalized Lasso, i.e., least squares minimization combined with a (convex) structural constraint. While Lasso-type estimators were originally designed for noisy linear regression problems, it has…
In a completely randomized experiment, the variances of treatment effect estimators in the finite population are usually not identifiable and hence not estimable. Although some estimable bounds of the variances have been established in the…
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…