Related papers: Uniform-in-Submodel Bounds for Linear Regression i…

We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…

Nonlinear expectation, including sublinear expectation as its special case, is a new and original framework of probability theory and has potential applications in some scientific fields, especially in finance risk measure and management.…

Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…

This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…

This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…

In this work, we consider a multivariate regression model with one-sided errors. We assume for the regression function to lie in a general H\"{o}lder class and estimate it via a nonparametric local polynomial approach that consists of…

In the classical setting of self-selection, the goal is to learn $k$ models, simultaneously from observations $(x^{(i)}, y^{(i)})$ where $y^{(i)}$ is the output of one of $k$ underlying models on input $x^{(i)}$. In contrast to mixture…

This paper analyzes the classical linear regression model with measurement errors in all the variables. First, we provide necessary and sufficient conditions for identification of the coefficients. We show that the coefficients are not…

Semi-functional linear regression models postulate a linear relationship between a scalar response and a functional covariate, and also include a non-parametric component involving a univariate explanatory variable. It is of practical…

Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…

We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix…

We consider the estimation problem in high-dimensional semi-supervised learning. Our goal is to investigate when and how the unlabeled data can be exploited to improve the estimation of the regression parameters of linear model in light of…

Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized…

A general class of models is proposed that is able to estimate the whole predictive distribution of a dependent variable $Y$ given a vector of explanatory variables $\xb$. The models exploit that the strength of explanatory variables to…

Estimating linear regression using least squares and reporting robust standard errors is very common in financial economics, and indeed, much of the social sciences and elsewhere. For thick tailed predictors under heteroskedasticity this…

Linear regression is a classical paradigm in statistics. A new look at it is provided via the lens of universal learning. In applying universal learning to linear regression the hypotheses class represents the label $y\in {\cal R}$ as a…

Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…

This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…

In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type…

It is clear that conventional statistical inference protocols need to be revised to deal correctly with the high-dimensional data that are now common. Most recent studies aimed at achieving this revision rely on powerful approximation…