Vasconcelos J C S, Cordeiro G M, Ortega E M M
ESALQ, Universidade de S ao Paulo, Piracicaba, Brazil.
UFPE, Universidade Federal de Pernambuco, Recife, Brazil.
J Appl Stat. 2020 Aug 7;49(1):248-267. doi: 10.1080/02664763.2020.1803812. eCollection 2022.
Semiparametric regressions can be used to model data when covariables and the response variable have a nonlinear relationship. In this work, we propose three flexible regression models for bimodal data called the additive, additive partial and semiparametric regressions, basing on the distribution under three types of penalized smoothers, where the main idea is not to confront the three forms of smoothings but to show the versatility of the distribution with three types of penalized smoothers. We present several Monte Carlo simulations carried out for different configurations of the parameters and some sample sizes to verify the precision of the penalized maximum-likelihood estimators. The usefulness of the proposed regressions is proved empirically through three applications to climatology, ethanol and air quality data.
当协变量和响应变量具有非线性关系时，半参数回归可用于对数据进行建模。在这项工作中，我们基于三种类型的惩罚平滑器下的分布，为双峰数据提出了三种灵活的回归模型，即加法回归、加法偏回归和半参数回归，其主要思想不是面对三种平滑形式，而是展示三种类型惩罚平滑器下分布的通用性。我们针对参数的不同配置和一些样本量进行了几次蒙特卡罗模拟，以验证惩罚最大似然估计器的精度。通过对气候学、乙醇和空气质量数据的三个应用，实证证明了所提出回归的有用性。
