We consider nonlinear heteroscedastic single‐index models where the mean function is a parametric nonlinear model and the variance function depends on a single‐index structure. We develop an efficient estimation method for the parameters in the mean function by using the weighted least squares estimation, and we propose a “delete‐one‐component” estimator for the single‐index in the variance function based on absolute residuals. Asymptotic results of estimators are also investigated. The estimation methods for the error distribution based on the classical empirical distribution function and an empirical likelihood method are discussed. The empirical likelihood method allows for incorporation of the assumptions on the error distribution into the estimation. Simulations illustrate the results, and a real chemical data set is analyzed to demonstrate the performance of the proposed estimators.

中文翻译：

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具有单指标异方差性的非线性回归模型

我们考虑非线性异方差单指数模型，其中均值函数是参数非线性模型，方差函数取决于单指数结构。我们通过使用加权最小二乘估计为均值函数中的参数开发了一种有效的估计方法，并且我们提出了一种基于绝对残差的方差函数中单指标的“删除一个分量”估计器。还研究了估计量的渐近结果。讨论了基于经典经验分布函数和经验似然法的误差分布估计方法。经验似然法允许将关于误差分布的假设纳入估计。模拟说明了结果，