异方差非线性回归模型(HNLM)是数据建模的重要工具。在本文中,我们提出了一种考虑正态(SSMN)分布的斜尺度混合的HNLM,这允许同时拟合非对称和重尾数据。通过期望最大化(EM)算法执行最大似然(ML)估计。观察到的信息矩阵是通过分析得出的,以考虑标准误差。此外,诊断分析是使用病例删除措施和局部影响方法开发的。进行了模拟研究,以验证似然比统计量的经验分布,方差检验的同质性和结构函数错误指定的研究。通过分析真实的数据集来说明所提出的方法。
The heteroscedastic nonlinear regression model (HNLM) is an important tool in data modeling. In this paper we propose a HNLM considering skew scale mixtures of normal (SSMN) distributions, which allows fitting asymmetric and heavy-tailed data simultaneously. Maximum likelihood (ML) estimation is performed via the expectation-maximization (EM) algorithm. The observed information matrix is derived analytically to account for standard errors. In addition, diagnostic analysis is developed using case-deletion measures and the local influence approach. A simulation study is developed to verify the empirical distribution of the likelihood ratio statistic, the power of the homogeneity of variances test and a study for misspecification of the structure function. The method proposed is also illustrated by analyzing a real dataset.