Varying coefficient model is often used in statistical modeling since it is more flexible than the parametric model. However, model detection and variable selection of varying coefficient model are poorly understood in mode regression. Existing methods in the literature for these problems are often based on mean regression and quantile regression. In this paper, we propose a novel method to solve these problems for mode varying coefficient model based on the B-spline approximation and SCAD penalty. Moreover, we present a new algorithm to estimate the parameters of interest, and discuss the parameters selection for the tuning parameters and bandwidth. We also establish the asymptotic properties of estimated coefficients under some regular conditions. Finally, we illustrate the proposed method by some simulation studies and an empirical example.

变系数模型常用于统计建模，因为它比参数模型更灵活。然而，模式回归中对变系数模型的模型检测和变量选择知之甚少。文献中针对这些问题的现有方法通常基于均值回归和分位数回归。在本文中，我们提出了一种基于 B 样条近似和 SCAD 惩罚的模式变系数模型解决这些问题的新方法。此外，我们提出了一种估计感兴趣参数的新算法，并讨论了调谐参数和带宽的参数选择。我们还建立了一些规则条件下估计系数的渐近性质。最后，我们通过一些模拟研究和一个实证例子来说明所提出的方法。