Abstract In the paper, the large deviation inequalities of the LS estimator for the nonlinear regression model with martingale differences errors are established. The assumptions for the errors are (conditional) exponential integrability which weaken the bounded condition in Hu (1993). As an application, we give the large deviation inequalities of LS estimator for the simple Michaelis–Menten model.

中文翻译：

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非线性回归模型中 LS 估计量的大偏差不等式

摘要 本文建立了具有鞅差误差的非线性回归模型的LS估计量的大偏差不等式。错误的假设是（条件）指数可积性，这削弱了 Hu (1993) 中的有界条件。作为一个应用，我们给出了简单 Michaelis-Menten 模型的 LS 估计量的大偏差不等式。