Statistics and Its Interface

Volume 11 (2018)

Number 1

Monotone function estimation in partially linear models

Pages: 19 – 29

DOI: http://dx.doi.org/10.4310/SII.2018.v11.n1.a2

Authors

Yi Zhang (School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China; and School of Insurance, Shanghai Lixin University of Accounting and Finance, Shanghai, China)

Shaoli Wang (School of Statistics and Management, Shanghai Key Laboratory of Financial Information Technology, Shanghai University of Finance and Economics, Shanghai, China)

Abstract

A kernel-based method is proposed for the monotone estimation of the nonparametric function component of a partially linear regression model. The estimated monotone function is constructed via a density estimate and numerical inversion. This procedure does not require constrained optimization and hence is fast to compute. Asymptotic normality is established for the proposed monotone function estimator. We apply the proposed method to analyze mammalian eye gene expression data and reveal a complex nonlinear relation within a gene network; we also analyze the German SOEP data using our method and validate the human capital theory.

Keywords

asymptotic normality, density estimation, kernel estimation, monotone function, nonparametric function, partially linear models

2010 Mathematics Subject Classification

62G05

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Yi Zhang’s research is partially supported by Graduate Innovation Foundation of Shanghai University of Finance and Economics, China (CXJJ-2014-460). Shaoli Wang’s research is partially supported by NSFC grant (11371235) and by Program for Innovative Research Team of Shanghai University of Finance and Economics.

Paper received on 17 August 2016.