ABSTRACT

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 odd log-logistic generalized inverse Gaussian 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.

摘要

当协变量和响应变量具有非线性关系时，可以使用半参数回归对数据进行建模。在这项工作中，我们提出了三种灵活的双峰数据回归模型，称为加性回归、加性部分回归和半参数回归，基于奇数对数逻辑广义逆高斯三种惩罚平滑器下的分布，其主要思想不是对抗三种形式的平滑，而是展示三种惩罚平滑器分布的多功能性。我们提出了几个针对不同参数配置和一些样本大小进行的蒙特卡罗模拟，以验证惩罚最大似然估计量的精度。通过对气候学、乙醇和空气质量数据的三个应用经验证明了所提出的回归的有用性。