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

TL;DR

This paper introduces a robust estimation and testing approach for nonlinear regression models, especially applied to enzyme kinetics, improving reliability in biochemical data analysis.

Contribution

It proposes a new robust estimation method based on minimum density power divergence for general NLR models, with theoretical and empirical validation.

Findings

The estimator is asymptotically normal and robust to outliers.

Simulation studies show improved efficiency and robustness.

Real data examples demonstrate practical applicability.

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.