Related papers: Testing Heteroskedasticity in High-Dimensional Lin…

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…

High-dimensional linear regression is a fundamental tool in modern statistics, particularly when the number of predictors exceeds the sample size. The classical Lasso, which relies on the squared loss, performs well under Gaussian noise…

We address the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor, where the joint distribution of the innovations is regarded an infinite-dimensional nuisance parameter. Using a…

A natural way of estimating heteroscedastic label noise in regression is to model the observed (potentially noisy) target as a sample from a normal distribution, whose parameters can be learned by minimizing the negative log-likelihood.…

This paper proposes self-normalized tests for multistep conditional predictive ability in forecast comparison. By normalizing the sample mean of the transformed loss differential using functionals of its cumulative sum (CUSUM) process,…

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…

Fitting high-dimensional statistical models often requires the use of non-linear parameter estimation procedures. As a consequence, it is generally impossible to obtain an exact characterization of the probability distribution of the…

The presence of outlying observations may adversely affect statistical testing procedures that result in unstable test statistics and unreliable inferences depending on the distortion in parameter estimates. In spite of the fact that the…

Linear regressions with endogeneity are widely used to estimate causal effects. This paper studies a framework that involves two common practical issues: endogeneity of the regressors and heteroskedasticity that depends on endogenous…

This paper explores testing unit roots based on least absolute deviations (LAD) regression under unconditional heteroskedasticity. We first derive the asymptotic properties of the LAD estimator for a first-order autoregressive process with…

This paper proposes a novel two-step strategy for testing the goodness-of-fit of parametric regression models in ultra-high dimensional sparse settings, where the predictor dimension far exceeds the sample size. This regime usually renders…

Let X; Z be r and s-dimensional covariates, respectively, used to model the response variable Y as Y = m(X;Z) + \sigma(X;Z)\epsilon. We develop an ANOVA-type test for the null hypothesis that Z has no influence on the regression function,…

After variable selection, standard inferential procedures for regression parameters may not be uniformly valid; there is no finite-sample size at which a standard test is guaranteed to approximately attain its nominal size. This problem is…

This article concerns tests for the two-sample location problem when the dimension is larger than the sample size. The traditional multivariate-rank-based procedures cannot be used in high dimensional settings because the sample scatter…

The Full Bayesian Significance Test (FBST) possesses many desirable aspects, such as dismissing the need for hypotheses to have positive prior probability and providing a measure of evidence against $H_0$. Still, few attempts have been made…

Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between…

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

The problems of Lasso regression and optimal design of experiments share a critical property: their optimal solutions are typically \emph{sparse}, i.e., only a small fraction of the optimal variables are non-zero. Therefore, the…

We consider the least-square linear regression problem with regularization by the l1-norm, a problem usually referred to as the Lasso. In this paper, we present a detailed asymptotic analysis of model consistency of the Lasso. For various…

A meta-model of the input-output data of a computationally expensive simulation is often employed for prediction, optimization, or sensitivity analysis purposes. Fitting is enabled by a designed experiment, and for computationally expensive…