Varying coefficient models (VCMs) allow us to generalise standard linear regression models to incorporate complex covariate effects by modelling the regression coefficients as functions of another covariate. For nonparametric varying coefficients, we can borrow the idea of parametrically guided estimation to improve asymptotic bias. In this paper, we develop a guided estimation procedure for the nonparametric VCMs. Asymptotic properties are established for the guided estimators and a method of bandwidth selection via bias-variance tradeoff is proposed. We compare the performance of the guided estimator with that of the unguided estimator via both simulation and real data examples.

中文翻译：

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具有拟似然的非参数变系数模型中的参数引导估计

可变系数模型 (VCM) 允许我们通过将回归系数建模为另一个协变量的函数来推广标准线性回归模型，以合并复杂的协变量效应。对于非参数变系数，我们可以借用参数引导估计的思想来改善渐近偏差。在本文中，我们为非参数 VCM 开发了一个引导估计程序。为引导估计器建立了渐近特性，并提出了一种通过偏差-方差权衡进行带宽选择的方法。我们通过模拟和真实数据示例将引导估计器的性能与非引导估计器的性能进行比较。