Efficient inference of longitudinal/functional data models with time‐varying additive structure

Abstract

AbstractIn the analysis of longitudinal or functional data, a time‐varying additive model (tvAM) has been introduced that is effective at avoiding the curse of dimensionality and capturing dynamic features. The present article focuses on the unified two‐step estimators of a tvAM with sparse or dense longitudinal or functional data. It is proved that the two‐step estimators have the same asymptotic distribution as that of oracle estimators. Furthermore, a unified convergence theory is established, based on which a unified inference is proposed without deciding whether the data are sparse or dense. Also, a testing statistic that can adapt to the sparse and dense cases in a unified framework is proposed to check whether the bivariate nonparametric functions are time varying, and the asymptotic distribution of the proposed test statistic is derived. Simulation studies are conducted to assess the finite‐sample performance of the proposed model and methods, and two different types of data are considered to illustrate the proposed method.