A Comparison of Estimators for a Two-Parameter Hyperbola

SUMMARY The hyperbola Y = Vx/(K+ x) occurs frequently in biochemistry (the Michaelis-Menten equation) and related subjects. The estimates of the parameters V and K obtained by the method of least squares (applied to both the observations and their logarithms) are compared with the conventional estimates from linear transformations by using simulated normally and lognormally distributed observations. With homoscedastic normal observations the least-squares (and thus maximum-likelihood) estimates of Vand Khave substantially smaller variance and less bias than the estimates from the best of the linear transformations unless the experimental results are very precise. When the coefficient of variation of the observations is constant none of the methods tested stands out as uniformly the best. There is a strong positive correlation between the estimates of V and K whichever method of estimation is used. 1. THE PROBLEM THE problem to be considered is how best to estimate the parameters, V and K, of the rectangular hyperbola Vx y Vx ~~~~~~~~~~(1)