Robust Inference for Non-Linear Regression Models with Applications in Enzyme Kinetics

Abstract: 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.