Related papers: Estimating grouped data models with a binary depen…
This article deals with asimple issue: if we have grouped data with a binary dependent variable and want to include fixed effects (group specific intercepts) in the specification, is Ordinary Least Squares (OLS) in any way superior to a…
Ordinary least squares (OLS) linear regression is one of the most basic statistical techniques for data analysis. In the main stream literature and the statistical education, the study of linear regression is typically restricted to the…
Ordinary least-squares (OLS) estimators for a linear model are very sensitive to unusual values in the design space or outliers among y values. Even one single atypical value may have a large effect on the parameter estimates. This article…
For multiple treatments D=0,1,...,J, covariates X and outcome Y, the ordinary least squares estimator (OLS) of Y on (D1,...,DJ,X) is widely applied to a constant-effect linear model, where Dj is the dummy variable for D=j. However, the…
In different fields of applications including, but not limited to, behavioral, environmental, medical sciences and econometrics, the use of panel data regression models has become increasingly popular as a general framework for making…
Linear regression is one of the most prevalent techniques in machine learning, however, it is also common to use linear regression for its \emph{explanatory} capabilities rather than label prediction. Ordinary Least Squares (OLS) is often…
We present a new finite-time analysis of the estimation error of the Ordinary Least Squares (OLS) estimator for stable linear time-invariant systems. We characterize the number of observed samples (the length of the observed trajectory)…
Least squares linear regression is one of the oldest and widely used data analysis tools. Although the theoretical analysis of the ordinary least squares (OLS) estimator is as old, several fundamental questions are yet to be answered.…
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…
I show that ordinary least squares (OLS) predictions can be rewritten as the output of a restricted attention module, akin to those forming the backbone of large language models. This connection offers an alternative perspective on…
This paper proposes a method for estimating multiple change points in panel data models with unobserved individual effects via ordinary least-squares (OLS). Typically, in this setting, the OLS slope estimators are inconsistent due to the…
This study investigated the problem posed by using ordinary least squares (OLS) to estimate parameters of simple linear regression under a specific context of special relativity, where an independent variable is restricted to an open…
Uncertainty in estimating the log-law parameters is arguably the greatest obstacle to establishing definitive conclusions regarding their numerical values and universality. This challenge is exacerbated by the limited number of studies that…
Regression is a fundamental tool in scientific research. Ordinary least squares (OLS), one of the most widely used regression methods, enjoys several desirable properties, including the best linear unbiased estimator (BLUE) property. It is…
The log transformation is widely used in linear regression, mainly because coefficients are interpretable as proportional effects. Yet this practice has fundamental limitations, most notably that the log is undefined at zero, creating an…
Ordinary least squares (OLS) is the default method for fitting linear models, but is not applicable for problems with dimensionality larger than the sample size. For these problems, we advocate the use of a generalized version of OLS…
Applied work often studies the effect of a binary variable ("treatment") using linear models with additive effects. I study the interpretation of the OLS estimands in such models when treatment effects are heterogeneous. I show that the…
A data analyst might worry about generalization if dropping a very small fraction of data points from a study could change its substantive conclusions. Checking this non-robustness directly poses a combinatorial optimization problem and is…
After performing a randomized experiment, researchers often use ordinary-least squares (OLS) regression to adjust for baseline covariates when estimating the average treatment effect. It is widely known that the resulting confidence…
We prove that the ordinary least-squares (OLS) estimator attains nearly minimax optimal performance for the identification of linear dynamical systems from a single observed trajectory. Our upper bound relies on a generalization of…