We revisit the second-order nonlinear least square estimator proposed in Wang and Leblanc (Anne Inst Stat Math 60:883–900, 2008) and show that the estimator reaches the asymptotic optimality concerning the estimation variability. Using a fully semiparametric approach, we further modify and extend the method to the heteroscedastic error models and propose a semiparametric efficient estimator in this more general setting. Numerical results are provided to support the results and illustrate the finite sample performance of the proposed estimator.

中文翻译：

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二阶非线性最小二乘估计器的效率及其扩展

我们重新审视了 Wang 和 Leblanc (Anne Inst Stat Math 60:883–900, 2008) 中提出的二阶非线性最小二乘估计量，并表明该估计量达到了关于估计变异性的渐近最优性。使用完全半参数的方法，我们进一步修改并将该方法扩展到异方差模型，并在这种更一般的设置中提出了一个半参数有效估计器。提供了数值结果以支持结果并说明所提出的估计器的有限样本性能。