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Nonlinear interaction detection through partial dimension reduction with missing response data

Hong-Xia Xu

Department of Mathematics, Shanghai Maritime University, Shanghai 201306, P. R. China

School of Data Sciences, Zhejiang University of Finance and Economics, Zhejiang 310018, P. R. China

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Guo-Liang Fan

https://orcid.org/0000-0002-9655-7545

School of Economics and Management, Shanghai Maritime University, Shanghai 201306, P. R. China

E-mail Address: glfan@shmtu.edu.cn

Corresponding author.

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, and

Jin-Chang Li

School of Data Sciences, Zhejiang University of Finance and Economics, Zhejiang 310018, P. R. China

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https://doi.org/10.1142/S2010326322500514Cited by:0 (Source: Crossref)

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.

Keywords:

AMSC: 62G05, 62G20

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