Although homoscedasticity is often assumed in linear regression, real data may show variance patterns or residual structures that violate this assumption. We propose VarGuid, a variance‐guided framework for two related settings: Covariate‐dependent conditional variance under a global linear mean model, and residual nonlinear mean structure that can mimic heteroscedasticity. The framework has two deliberately separated components. The first uses an iteratively reweighted regression (IRR) algorithm to estimate a sparse global linear mean–variance model and support coefficient interpretation. The second uses a biconvex artificial‐grouping algorithm for conditional prediction, keeping the fitted linear backbone fixed while adding group‐specific local intercept corrections. We establish predictive‐risk guarantees for the global estimator, and simulations and empirical studies show improved out‐of‐sample accuracy. VarGuid is illustrated in two applications: Health‐related quality of life in low‐ and middle‐income countries, and high‐dimensional genomic prediction of lymph node evaluation in breast cancer.
- Variance‐Guided Regression for Heteroscedastic Data With a Grouping‐Based Extension for Nonlinear Prediction
- Sibei Liu - University of MiamiMin Lu - University of Miami
- Statistics in medicine, Vol.45(13-14), p.e70632
- WILEY; HOBOKEN
- 14
- National Heart, Lung, and Blood Institute: R01 HL164405 Medical Research Council: MR/P008984/1 National Institute of General Medical Sciences: R35 GM139659
This work was supported by the National Institute of General Medical Sciences of the National Institutes of Health (Grant No. R35 GM139659); the National Heart, Lung, and Blood Institute of the National Institutes of Health (Grant No. R01 HL164405); and the Medical Research Council (Grant No. MR/P008984/1) under a Global Alliance for Chronic Disease call, and the 2023 Relief Funding Award from the Office of the Vice Provost for Research and Scholarship and the Office of Faculty Affairs, University of Miami.
- Miller School of Medicine; UMMG Department of Public Health Sciences Research
- English
- Journal article
- 42252209
- 991033108095402976