Network-adaptive robust penalized estimation of time-varying coefficient models with longitudinal data

Abstract

Longitudinal data are commonly encountered in many fields. Many statistical models have been developed, among which the time-varying coefficient model has been shown to be effective for many practical problems. Long-tailed/contaminated distributions are not uncommon and cannot be accommodated using non-robust likelihood-based estimation. Another common limitation shared by many of the existing methods is the insufficient account for the interconnections among covariates. In this study, we adopt a least absolute deviation loss function to achieve robustness. For the selection of relevant covariates, a penalization approach is adopted. Significantly advancing from the existing literature, we describe the interconnections among covariates using a network structure and develop novel penalties to accommodate the network connectivity and connection measures. Consistency properties are rigorously established. Numerical studies, including both simulations and data analysis, demonstrate the competitive practical performance of the proposed method.