Efficient Spline Estimation of Nonparametric Additive Functions with Repeated Measures

• Activity Number: 504
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Rong Liu*+ and Rong Liu
• Companies: University of Toledo and University of Toledo
• Keywords: B spline ; Clustered data ; Longitudinal data ; additive model ; smoothing

Abstract

There has been substantial recent interest in developing nonparametric and semiparametric regression methods for longitudinal/clustered data. While there is a considerable literature in the scalar covariate case, the problem has been addressed very few in the multivariate additive model case. Carroll et al (2009) represents a first contribution in this direction and kernel smoothing is used. Kernel methods are mathematically convenient but extremely computationally intensive when either the dimension is high or sample size is large. The other popular approaches, spline methods, are fast to compute but lack limiting distribution. We proposes to use spline-backfitted spline estimator, which is both computationally efficient and theoretically reliable, to derive the asymptotic normal distributions of the estimation of nonparametric component functions. Simulated examples are provided to illustrate the theoretical properties.