Nonlinear interaction detection through partial dimension reduction with missing response data

Abstract

In this paper, we are concerned with nonlinear interaction detection based on partial dimension reduction with missing response data. The covariates are grouped through linear combinations in a general class of semi-parametric models to detect their joint interaction effects. The joint interaction effects are estimated by a profile least squares approach with the help of the inverse probability weighted technique. The asymptotic properties of the resulting estimate for the central partial mean subspace are established. In addition, a Wald type test is proposed to detect the interactions between the covariates. A BIC-type criterion is applied to determine the structural dimension of the central partial mean subspace and its consistency is also obtained. Simulations are conducted to examine the finite sample performances of our proposed method and a real data set is analyzed for illustration.