Semiparametric estimation of multivariate partially linear models

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.