Despite linear regression being the most popular statistical modelling technique, in real-life we often need to deal with situations where the true relationship between the response and the covariates is nonlinear in parameters. In such cases one needs to adopt appropriate non-linear regression (NLR) analysis, having wider applications in biochemical and medical studies among many others. In this paper we propose a new improved robust estimation and testing methodologies for general NLR models based on the minimum density power divergence approach and apply our proposal to analyze the widely popular Michaelis-Menten (MM) model in enzyme kinetics. We establish the asymptotic properties of our proposed estimator and tests, along with their theoretical robustness characteristics through influence function analysis. For the particular MM model, we have further empirically justified the robustness and the efficiency of our proposed estimator and the testing procedure through extensive simulation studies and several interesting real data examples of enzyme-catalyzed (biochemical) reactions.

翻译：尽管线性回归是最流行的统计建模技术，但在实际应用中，我们常常需要处理响应变量与协变量之间的真实关系在参数上呈非线性的情况。此时，需要采用适当的非线性回归分析，该方法在生物化学和医学研究等众多领域具有广泛的应用。本文基于最小密度功率散度方法，为一般非线性回归模型提出了一种新的改进型稳健估计与检验方法，并将我们的方案应用于分析酶动力学中广泛使用的米氏模型。我们通过影响函数分析，建立了所提估计量与检验的渐近性质及其理论稳健性特征。针对特定的米氏模型，我们通过大量的模拟研究以及酶催化（生物化学）反应的多个有趣实际数据案例，进一步从实证角度验证了所提估计量与检验程序的稳健性和有效性。