Related papers: Unlocking the Regression Space
We establish oracle inequalities for a version of the Lasso in high-dimensional fixed effects dynamic panel data models. The inequalities are valid for the coefficients of the dynamic and exogenous regressors. Separate oracle inequalities…
This paper studies linear time series regressions with many regressors. Weak exogeneity is the most used identifying assumption in time series. Weak exogeneity requires the structural error to have zero conditional expectation given the…
A robust estimation framework for binary regression models is studied, aiming to extend traditional approaches like logistic regression models. While previous studies largely focused on logistic models, we explore a broader class of models…
Under the Neyman causal model, it is well-known that OLS with treatment-by-covariate interactions cannot harm asymptotic precision of estimated treatment effects in completely randomized experiments. But do such guarantees extend to…
In the early 1980s Halbert White inaugurated a "model-robust'' form of statistical inference based on the "sandwich estimator'' of standard error. This estimator is known to be "heteroskedasticity-consistent", but it is less well-known to…
Many models for sparse regression typically assume that the covariates are known completely, and without noise. Particularly in high-dimensional applications, this is often not the case. This paper develops efficient OMP-like algorithms to…
In this study, we propose a general model capable of addressing heterogeneity in higher-order moments while preserving mean and variance, including the t, Laplace, and skew-normal distributions as special cases. Our model flexibly…
This paper proposes a class of parametric multiple-index time series models that involve linear combinations of time trends, stationary variables and unit root processes as regressors. The inclusion of the three different types of time…
For learned models to be trustworthy, it is essential to verify their robustness to perturbations in the training data. Classical approaches involve uncertainty quantification via confidence intervals and bootstrap methods. In contrast,…
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…
We present a comprehensive framework for applying rigorous statistical techniques from econometrics to analyze and improve machine learning systems. We introduce key statistical methods such as Ordinary Least Squares (OLS) regression,…
Ordinary least square (OLS), maximum likelihood (ML) and robust methods are the widely used methods to estimate the parameters of a linear regression model. It is well known that these methods perform well under some distributional…
Ordinary Differential Equations (ODEs) have recently gained a lot of attention in machine learning. However, the theoretical aspects, e.g., identifiability and asymptotic properties of statistical estimation are still obscure. This paper…
In the heteroscedastic linear model, the weighted least squares (WLS) estimate of the model coefficients is more efficient than the ordinary least squares (OLS) esti- mate. However, the practical application of WLS is challenging because it…
In this paper we discuss the variable selection method from \ell0-norm constrained regression, which is equivalent to the problem of finding the best subset of a fixed size. Our study focuses on two aspects, consistency and computation. We…
The main object of investigation in this paper is a very general regression model in optional setting - when an observed process is an optional semimartingale depending on an unknown parameter. It is well-known that statistical data may…
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…
We propose the orthogonal random forest, an algorithm that combines Neyman-orthogonality to reduce sensitivity with respect to estimation error of nuisance parameters with generalized random forests (Athey et al., 2017)--a flexible…
Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the…
We collect robust proposals given in the field of regression models with heteroscedastic errors. Our motivation stems from the fact that the practitioner frequently faces the confluence of two phenomena in the context of data analysis:…