Robust and efficient estimator for simultaneous model structure identification and variable selection in generalized partial linear varying coefficient models with longitudinal data

This paper proposes a new robust and efficient estimator for the generalized partial linear varying coefficient models with longitudinal data, which can construct variable selection and partial linear structure identification simultaneously. The new method is built upon a newly proposed smooth-threshold robust and efficient generalized estimating equations, which can use the within subject correlation structure, and achieves robustness against outliers by using bounded exponential score function and leverage-based weights. By introducing an additional tuning parameter, it has balance between robustness and efficiency. Under mild conditions, we prove that, with probability tending to one, it can select the relevant variables and identify the partial linear structure correctly. Furthermore, the varying and nonzero constant coefficients can be estimated accurately, just as the true model structure and relevant variables were known in advance. Simulation studies and real data analysis also confirm our method.