Robust Estimation in Enzyme Kinetics

Abstract

Although the method of least squares is optimal for fitting equations to data under idealized conditions, it gives poor results if these conditions are violated. It is highly sensitive to the presence of outliers in the data and it requires correct weighting. The direct linear plot is a method of plotting the Michaelis-Menten equation in parameter space that leads to robust estimates of the parameters, i.e., estimates based on few assumptions about the statistical structure of the data. It performs well with the Michaelis-Menten equation, and similar methods can be applied with equal success to other two-parameter models, but it cannot easily be applied to models with more than two parameters to be estimated. For this reason there is interest in other robust methods, such as biweight regression, which resembles least-squares regression in which decreased or zero weight is assigned to outlying observations. Such methods provide good protection against outliers but need correct weights to work satisfactorily.