Related papers: A bias test for heteroscedastic linear least-squar…
This paper provides an alternative to penalized estimators for estimation and vari- able selection in high dimensional linear regression models with measurement error or missing covariates. We propose estimation via bias corrected least…
Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…
Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the…
Many core concepts in political science are latent and therefore can only be measured with error. Measurement error in a predictor attenuates slope coefficient estimates in regression, biasing them toward zero. We show that widely used…
Given a linear regression setting, Iterative Least Trimmed Squares (ILTS) involves alternating between (a) selecting the subset of samples with lowest current loss, and (b) re-fitting the linear model only on that subset. Both steps are…
Sample complexity of bias estimation is a lower bound on the runtime of any bias detection method. Many regulatory frameworks require the bias to be tested for all subgroups, whose number grows exponentially with the number of protected…
Least-squares refitting is widely used in high dimensional regression to reduce the prediction bias of l1-penalized estimators (e.g., Lasso and Square-Root Lasso). We present theoretical and numerical results that provide new insights into…
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…
Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and their asymptotic normality are…
A weighted regression procedure is proposed for regression type problems where the innovations are heavy-tailed. This method approximates the least absolute regression method in large samples, and the main advantage will be if the sample is…
Subsampling methods have been recently proposed to speed up least squares estimation in large scale settings. However, these algorithms are typically not robust to outliers or corruptions in the observed covariates. The concept of influence…
The nested error regression model is a useful tool for analyzing clustered (grouped) data, and is especially used in small area estimation. The classical nested error regression model assumes normality of random effects and error terms, and…
The Bayes linear estimator is derived by minimizing the Bayes risk with respect to the squared loss function. Non-unbiased estimators such as ordinary ridge, typical shrinkage, fractional rank, and restricted least squares estimators, as…
In this paper, we consider the extent of the biases that may arise when an unmeasured confounder is omitted from a structural equation model (SEM) and we propose sensitivity analysis techniques to correct for such biases. We give an…
Prediction with the possibility of abstention (or selective prediction) is an important problem for error-critical machine learning applications. While well-studied in the classification setup, selective approaches to regression are much…
Error-in-variables regression is a common ingredient in treatment effect estimators using panel data. This includes synthetic control estimators, counterfactual time series forecasting estimators, and combinations. We study high-dimensional…
Linear regression models are checked by a lack-of-fit (LOF) test to be sure that the model is at least approximatively true. In many practical cases data are sampled sequentially. Such a situation appears in industrial production when goods…
Measuring the stability of conclusions derived from Ordinary Least Squares linear regression is critically important, but most metrics either only measure local stability (i.e. against infinitesimal changes in the data), or are only…
In this article we study the asymptotic behaviour of the least square estimator in a linear regression model based on random observation instances. We provide mild assumptions on the moments and dependence structure on the randomly spaced…
We propose an empirical likelihood ratio test for nonparametric model selection, where the competing models may be nested, nonnested, overlapping, misspecified, or correctly specified. It compares the squared prediction errors of models…