Semi-nonparametric Varying Coefficients Models

Motivated by imaging genetics, this paper introduces a semi-nonparametric varying coefficients modeling framework to reveal varying associations between genetic markers and imaging responses.We aim to conduct a comprehensive theoretical analysis of estimation and inference procedures applicable to these models.By employing the kernel machine method, we estimate unknown varying coefficient functions and derive their representer theorem.We also establish the theoretical properties of these estimated functions, including their rate of convergence, Bahadur representation, point-wise limit distributions, and confidence intervals.Additionally, we propose test statistics under a linear mixed effects model framework to assess the significance of all varying coefficients, taking into account within-subject dependence.The efficacy of our proposed methodology is demonstrated through simulation studies and an application to data from the