Nonparametric and Semiparametric Methods for Longitudinal Data Analysis

University Of Pennsylvania, Philadelphia PA

Investigators

Abstract

Abstract DMS-0204556 PI: Jianhua Huang Longitudinal data, which involve variables observed repeatedly over time, are common in biomedicine, epidemiology, economics, sociology, and many other fields. Nonparametric and semiparametric statistical methods provide effective tools for extracting useful information from this type of data. These methods allow scientists, policy makers and researchers to draw conclusions from their data without depending on pre-specified assumptions that may be too restrictive to their settings. The objective of this proposal is to develop systematic, theoretically well-founded, and more efficient such methods. The focus is on the following five topics: (i) further theoretical and methodological development of the spline-based approach to time-varying coefficient models; (ii) estimation of covariance structures; (iii) extension of time-varying coefficient models to generalized linear models; (iv) extension of time-varying coefficient models to take into account accumulative covariate effects; (v) semiparametric efficient estimation in partly linear models. These projects involve developing novel estimation and inference procedures, providing theoretical justification, and discussing their theoretical and practical importance to the advancement of biomedical and statistical science. The research approach will be a combination of theoretical asymptotic analysis, Monte Carlo simulations and real data analysis. Global smoothing techniques with spline functions will be used.