Variance-Guided Regression for Heteroscedastic Data: Estimation and Application in Health Studies

Music City Center 

Homoscedasticity is a key assumption in traditional linear models, but it is frequently violated in real-world data, leading to biased coefficient estimates and incorrect inference. This paper introduces variance-guided (VarGuid) regression, a method designed to improve coefficient estimation and uncertainty quantification under heteroscedastic conditions. VarGuid employs an iteratively reweighted least squares approach that integrates data-adaptive weights to account for varying conditional variance structures. We derive the maximum likelihood estimator for the model parameters and demonstrate its theoretical properties. Through simulation studies, we demonstrate that VarGuid provides more accurate coefficient estimates and better confidence interval coverage compared to Ordinary Least Squares in the presence of heteroscedasticity. Additionally, we apply VarGuid to a real-world dataset analyzing factors associated with respiratory-related quality of life in low- and middle-income countries. Our findings highlight the advantages of VarGuid in improving estimation accuracy and inference reliability for heteroscedastic data.

Heteroscedasticity

Maximum likelihood estimation

Nonlinearity