Souza Vasconcelos Julio Cezar, Villegas Cristian
University of São Paulo, Piracicaba, Brazil.
J Appl Stat. 2020 Feb 12;48(3):557-572. doi: 10.1080/02664763.2020.1726301. eCollection 2021.
In this work, we propose a new model called generalized symmetrical partial linear model, based on the theory of generalized linear models and symmetrical distributions. In our model the response variable follows a symmetrical distribution such a normal, Student-t, power exponential, among others. Following the context of generalized linear models we consider replacing the traditional linear predictors by the more general predictors in whose case one covariate is related with the response variable in a non-parametric fashion, that we do not specified the parametric function. As an example, we could imagine a regression model in which the intercept term is believed to vary in time or geographical location. The backfitting algorithm is used for estimating the parameters of the proposed model. We perform a simulation study for assessing the behavior of the penalized maximum likelihood estimators. We use the quantile residuals for checking the assumption of the model. Finally, we analyzed real data set related with pH rivers in Ireland.
在这项工作中，我们基于广义线性模型理论和对称分布提出了一种名为广义对称部分线性模型的新模型。在我们的模型中，响应变量遵循诸如正态、学生t分布、幂指数分布等对称分布。在广义线性模型的背景下，我们考虑用更一般的预测变量取代传统的线性预测变量，在这种情况下，一个协变量以非参数方式与响应变量相关，我们没有指定参数函数。例如，我们可以设想一个回归模型，其中截距项被认为会随时间或地理位置而变化。使用反向拟合算法来估计所提出模型的参数。我们进行了一项模拟研究，以评估惩罚最大似然估计量的性能。我们使用分位数残差来检验模型的假设。最后，我们分析了与爱尔兰河流pH值相关的真实数据集。
