A Hybrid Omnibus Test for Generalized Partial Linear Single Index Model

• Activity Number: 484
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yangyi Xu*+ and Inyoung Kim and Raymond J. Carroll
• Companies: Virginia Tech and Virginia Tech and Texas A&M University
• Keywords: Hybrid ; Omnibus ; Score ; Single index ; Spline Approximation

Abstract

In this paper we propose Freqentist-Bayesian hybrid score-type omnibus tests for a functional generalized partial linear single index model where we model with link being a function of a generalized partially linear single index model. Our approach is developed in the semiparametric model framework where no likelihood function is available. We propose an efficient score to avoid likelihood derivation and then construct its asymptotic distribution. Using this score, we develop our hybrid omnibus tests based on splines as well as orthogonal series approximation. We compare our approaches with a likelihood ratio test using simulation study. Our simulation results suggest that our approaches outperforms in terms of size, power, and computation cost. The advantage of our approach is also demonstrated using a genetic pathway data of type II diabetes.