Filling and D -optimal designs for the correlated generalized exponential models

The aim of this paper is to provide guidelines for the statistically efficient estimation of parameters of a modified Arrhenius model for chemical kinetics. A modified Arrhenius model is used for instance by modeling a flux of methane in troposphere or by chemical kinetics for reactions at membranes. D -optimal and filling designs for the Generalized Exponential Model with correlated observations are studied, considering the exponential covariance with or without nugget effect. Both equidistant and exact designs for small samples are examined, studying the behavior of different types of filling designs when a greater number of observations is preferred. Probably the main lesson we can learn is that the D -optimal design is analytically peculiar and these designs can be practically obtained only by numerical computation; however, specially two point locally D -optimal designs are very interesting, since they may help us to find a reasonable range for filling designs. The latter ones are probably only applicable when seeking for a higher number of design points. It is an interesting issue that very often the best designs do not use the whole design interval, but only a part of it; this should be taken into account by practitioners when they design their experiments. The second important observation is the large bias of the ML estimator of the correlation parameter. From the theoretical point of view this is not surprising since variance and correlation parameters are not simultaneously identifiable. We develop a bias reduction method and illustrate its effectiveness. We also provide practical implications for chemometrics.