Related papers: Measurement Error in Lasso: Impact and Correction

Conformal prediction is a general method that converts almost any point predictor to a prediction set. The resulting set keeps good statistical properties of the original estimator under standard assumptions, and guarantees valid average…

Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…

The lasso is a popular method to induce shrinkage and sparsity in the solution vector (coefficients) of regression problems, particularly when there are many predictors relative to the number of observations. Solving the lasso in this…

Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant…

We revisit the adaptive Lasso as well as the thresholded Lasso with refitting, in a high-dimensional linear model, and study prediction error, $\ell_q$-error ($q \in \{1, 2 \} $), and number of false positive selections. Our theoretical…

Spatial microeconometric studies typically suffer from various forms of inaccuracies that are not present when dealing with the classical regional spatial econometrics models. Among those, missing data, locational errors, sampling without a…

The lasso and related sparsity inducing algorithms have been the target of substantial theoretical and applied research. Correspondingly, many results are known about their behavior for a fixed or optimally chosen tuning parameter specified…

We address measurement error bias in propensity score (PS) analysis due to covariates that are latent variables. In the setting where latent covariate $X$ is measured via multiple error-prone items $\mathbf{W}$, PS analysis using several…

Quantile regression is a very important tool to explore the relationship between the response variable and its covariates. Motivated by mean regression with LASSO for compositional covariates proposed by Lin et al. (2014), we consider…

Blocking, a special case of rerandomization, is routinely implemented in the design stage of randomized experiments to balance the baseline covariates. This study proposes a regression adjustment method based on the least absolute shrinkage…

Model selection in penalized regression critically depends on an accurate assessment of model complexity, commonly quantified through the effective degrees of freedom. While the Lasso admits a simple and unbiased characterization, given by…

A key challenge in environmental health research is unmeasured spatial confounding, driven by unobserved spatially structured variables that influence both treatment and outcome. A common approach is to fit a spatial regression that models…

Estimation of a precision matrix (i.e., inverse covariance matrix) is widely used to exploit conditional independence among continuous variables. The influence of abnormal observations is exacerbated in a high dimensional setting as the…

In a linear instrumental variables (IV) setting for estimating the causal effects of multiple confounded exposure/treatment variables on an outcome, we investigate the adaptive Lasso method for selecting valid instrumental variables from a…

I briefly report on some unexpected results that I obtained when optimizing the model parameters of the Lasso. In simulations with varying observations-to-variables ratio n=p, I typically observe a strong peak in the test error curve at the…

Selective inference methods are developed for group lasso estimators for use with a wide class of distributions and loss functions. The method includes the use of exponential family distributions, as well as quasi-likelihood modeling for…

Tens of thousands of simultaneous hypothesis tests are routinely performed in genomic studies to identify differentially expressed genes. However, due to unmeasured confounders, many standard statistical approaches may be substantially…

This paper is concerned with high-dimensional error-in-variables regression that aims at identifying a small number of important interpretable factors for corrupted data from many applications where measurement errors or missing data can…

We propose a new method of learning a sparse nonnegative-definite target matrix. Our primary example of the target matrix is the inverse of a population covariance or correlation matrix. The algorithm first estimates each column of the…

Random forests are a statistical learning technique that use bootstrap aggregation to average high-variance and low-bias trees. Improvements to random forests, such as applying Lasso regression to the tree predictions, have been proposed in…