In this paper, we consider the situation in which the observations follow an isotonic generalized partly linear model. Under this model, the mean of the responses is modelled, through a link function, linearly on some covariates and nonparametrically on an univariate regressor in such a way that the nonparametric component is assumed to be a monotone function. A class of robust estimates for the monotone nonparametric component and for the regression parameter, related to the linear one, is defined. The robust estimators are based on a spline approach combined with a score function which bounds large values of the deviance. As an application, we consider the isotonic partly linear log-Gamma regression model. Under regularity conditions, we derive consistency results for the nonparametric function estimators as well as consistency and asymptotic distribution results for the regression parameter estimators. Besides, the empirical influence function allows us to study the sensitivity of the estimators to anomalous observations. Through a Monte Carlo study, we investigate the performance of the proposed estimators under a partly linear log-Gamma regression model with increasing nonparametric component. The proposal is illustrated on a real data set.

中文翻译：

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单调约束下广义局部线性回归模型的鲁棒估计

在本文中，我们考虑了观测遵循等渗广义部分线性模型的情况。在此模型下，通过链接函数对某些协变量进行线性建模，对单变量回归进行非参数化建模，从而将响应的平均值建模为非参数分量被视为单调函数。定义了与线性相关的单调非参数分量和回归参数的一类鲁棒估计。鲁棒的估计器基于样条曲线方法，并结合了界定较大偏差值的得分函数。作为应用，我们考虑等渗的部分线性对数-Gamma回归模型。在正常情况下 我们导出非参数函数估计量的一致性结果以及回归参数估计量的一致性和渐近分布结果。此外，经验影响函数使我们能够研究估计量对异常观测值的敏感性。通过蒙特卡洛研究，我们在具有增加的非参数成分的部分线性对数-Gamma回归模型下调查了拟议估计量的性能。该提案在真实数据集上进行了说明。我们在具有增加的非参数成分的部分线性对数-Gamma回归模型下调查拟议估计量的性能。该提案在真实数据集上进行了说明。我们在具有增加的非参数成分的部分线性对数-Gamma回归模型下调查拟议估计量的性能。该提案在真实数据集上进行了说明。