Related papers: Sparse Linear Models and Two-Stage Estimation in H…

Economic modeling in the presence of endogeneity is subject to model uncertainty at both the instrument and covariate level. We propose a Two-Stage Bayesian Model Averaging (2SBMA) methodology that extends the Two-Stage Least Squares (2SLS)…

Mixed linear regression (MLR) has attracted increasing attention because of its great theoretical and practical importance in capturing nonlinear relationships by utilizing a mixture of linear regression sub-models. Although considerable…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…

In this paper, we propose a new method for estimation and constructing confidence intervals for low-dimensional components in a high-dimensional model. The proposed estimator, called Constrained Lasso (CLasso) estimator, is obtained by…

We show by simulation that the test for an unknown threshold in models with endogenous regressors - proposed in Caner and Hansen (2004) - can exhibit severe size distortions both in small and in moderately large samples, pertinent to…

The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of…

We consider the linear regression model with observation error in the design. In this setting, we allow the number of covariates to be much larger than the sample size. Several new estimation methods have been recently introduced for this…

High-dimensional settings, where the data dimension ($d$) far exceeds the number of observations ($n$), are common in many statistical and machine learning applications. Methods based on $\ell_1$-relaxation, such as Lasso, are very popular…

In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated…

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…

In a high dimensional regression setting in which the number of variables ($p$) is much larger than the sample size ($n$), the number of possible two-way interactions between the variables is immense. If the number of variables is in the…

This paper concerns the estimation of linear panel data models with endogenous regressors and a latent group structure in the coefficients. We consider instrumental variables estimation of the group-specific coefficient vector. We show that…

High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…

This paper proposes a bootstrap-assisted procedure to conduct simultaneous inference for high dimensional sparse linear models based on the recent de-sparsifying Lasso estimator (van de Geer et al. 2014). Our procedure allows the dimension…

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…

This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…

In this paper, we study the problem of sparse mean estimation under adversarial corruptions, where the goal is to estimate the $k$-sparse mean of a heavy-tailed distribution from samples contaminated by adversarial noise. Existing methods…

We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…

High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain…