On curvature measurements of the nonlinear errors in variable models by application study

Abstract

Relative curvature measurements are of great importance from a practical point of view since it determines the validity of the linearized approximation used in estimation problems for nonlinear regression models. But, these measurements can be negatively affected when an explanatory variable contains a measurement error as well as response variables and can prevent accurate inferences. In our study, we considered the curvature measurement of nonlinear errors in variable models to investigate adequacy of the linear approximation in case the explanatory variables are subjected to measurement error and how the parameter estimation problem is affected by this error, using the geometric concepts such as parameter-effects and intrinsic curvatures of the model function. Then, for the two cases of the explanatory variable, curvature calculations and statistical inferences were made on the chemical model called Michaelis-Menten, in which the rate of reaction against a substrate concentration is measured, by using different data sets.