Additive Modeling for Longitudinal Data via Classical Backfitting

• Activity Number: 616 - New Advances in Semiparametric Modeling and Testing for Complex Data
• Type: Topic Contributed
• Date/Time: Thursday, August 2, 2018 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Suneel Babu Chatla* and Li-Shan Huang
• Companies: and Institute of Statistics, National Tsing Hua University, TAIWAN
• Keywords: Smooth backfitting; Cholesky decomposition; Linear smoothers; Within correlation

Abstract

We propose a new classical backfitting framework for estimating an additive model for the unbalanced longitudinal data. We use Choleksy decomposition method to adjust for the correlations among repeated measurements which in turn enables us to extend the cross sectional backfitting methods such as classical backfitting and smooth backfitting to estimate the additive model in longitudinal data. We derive the asymptotic properties of the estimates obtained from the proposed classical backfitting algorithm. Our theoretical results illustrate that the backfitting estimators achieve the oracle bias and variance properties under some regularity conditions. Further, we also show that the updates in smooth backfitting algorithm are equivalent to the updates in the proposed classical backfitting algorithm. Our numerical comparison also illustrates that the proposed method achieves efficiency gain over the working independence model even in finite samples. A real data application is also provided to illustrate the usefulness of the estimation procedure proposed.