Unified inference for quantile varying coefficient models with longitudinal/functional data

Time varying coefficient models are widely employed in the realm of longitudinal and functional data analysis. The present paper primarily concentrates on quantile regression in time varying coefficient models, without making any assumptions about the error distribution or intra-subject dependence structure. Although the estimation process traditionally involves discontinuous indicator functions, we choose to employ smoothed estimating equations instead. We demonstrate that when the local linear method is utilised to estimate the undisclosed functions in time-varying coefficient models, for both sparse and dense longitudinal/functional data, the asymptotic results differ significantly between sparse and dense longitudinal/functional data scenarios. Leveraging the smoothed estimating equations, we retrieve a ‘sandwich’ formula for variance estimation and formulate methodologies that can acclimatise to both sparse and dense situations within a unified paradigm. To demonstrate the effectiveness of the proposed unified inference method, we conduct simulation studies and two real data analyses.