626 citations · 1.4k across the 31 of their papers we have counts for
20 papers · 1 filter
Ensemble minimaxity of James-Stein estimators
Yuzo Maruyama, Lawrence D. Brown, Edward I. George
This article discusses estimation of a multivariate normal mean based on heteroscedastic observations. Under heteroscedasticity, estimators shrinking more on the coordinates with l…
All of Linear Regression
Arun K. Kuchibhotla, Lawrence D. Brown, Andreas Buja +1
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,…
Model-free Study of Ordinary Least Squares Linear Regression
Arun K. Kuchibhotla, Lawrence D. Brown, Andreas Buja
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 s…
Uniform-in-Submodel Bounds for Linear Regression in a Model Free Framework
Arun Kumar Kuchibhotla, Lawrence D. Brown, Andreas Buja +2
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulne…
Models as Approximations II: A Model-Free Theory of Parametric Regression
Andreas Buja, Lawrence Brown, Arun Kumar Kuchibhotla +3
We develop a model-free theory of general types of parametric regression for iid observations. The theory replaces the parameters of parametric models with statistical functionals,…
Semi-Supervised linear regression
David Azriel, Lawrence D. Brown, Michael Sklar +3
We study a regression problem where for some part of the data we observe both the label variable () and the predictors (), while for other part of the data only the pre…