Generalized additive partial linear models for analyzing correlated data

Statistical procedures are proposed in generalized additive partial linear models (GAPLM) for analyzing correlated data. A reweighed iterative process based on the backfitting algorithm is derived for the parameter estimation from a penalized GEE. Discussions on the inferential aspects of GAPLM, particularly on the asymptotic properties of the former estimators as well as on the effective degrees of freedom derivation, are given. Diagnostic methods, such as leverage measures, residual analysis and local influence graphs, under different perturbation schemes, are proposed. A small simulation study is performed to assess the empirical distribution of the parametric and nonparametric estimators as well as of some proposed residuals. Finally, a motivating data set is analyzed by the methodology developed through the paper.