Semiparametric estimation of multivariate partially linear models

ABSTRACT

Inspired by a primary hypertension study was conducted by Chinese government in the Inner Mongolia Autonomous Region, we introduce partially linear models with multivariate responses to evaluate the simultaneous effects of modifiable risk factors on both the systolic and the diastolic blood pressures. We propose a class of weighted profile least-squares approaches to estimate both the parametric and the nonparametric components of the multivariate partially linear models. We also investigate how the weight matrix affects the resultant estimation efficiency. We illustrate our proposals through simulations and an analysis of the primary hypertension data. Our analysis provides strong evidence that the obesity is indeed an important risk factor predisposing to primary hypertension even after adjusting for the ageing effect.

KEYWORDS:

• Multivariate response
• partially linear models
• primary hypertension
• relative efficiency
• semiparametric estimation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China (Nos. 11371236 and 11422107), Henry Fok Education Foundation Fund of Young College Teachers (No. 141002) and Innovative Research Team in University of China the MOE Project of Key Research Institute of Humanities and Social Sciences at Universities (16JJD910002) and National Youth Top-notch Talent Support Program, China, Shanghai University of Finance and Economics Innovation Fund of Graduate Student (IRT13077), Ministry of Education of China, Shanghai University of Finance and Economics Innovation Fund of Graduate Student (CXJJ-2014-450).