Abstract

GAVIRIA, JAIME ANDRÉS  and  LOPEZ-RIOS, VÍCTOR IGNACIO. Locally D-Optimal Designs with Heteroscedasticity: A Comparison between Two Methodologies. Rev.Colomb.Estad. [online]. 2014, vol.37, n.1, pp.95-110. ISSN 0120-1751.  https://doi.org/10.15446/rce.v37n1.44360.

The classic theory of optimal experimental designs assumes that the errors of the model are independent and have a normal distribution with constant variance. However, the assumption of homogeneity of variance is not always satisfied. For example when the variability of the response is a function of the mean, it is probably that a heterogeneity model be more adequate than a homogeneous one. To solve this problem there are two methods: The first one consists of incorporating a function which models the error variance in the model, the second one is to apply some of the Box-Cox transformations to both sides on the nonlinear regression model to achieve a homoscedastic model (R.J. Carroll & D. Ruppert 1988, Chapter 4). In both cases it is possible to find the optimal design but the problem becomes more complex because it is necessary to find an expression for the Fisher information matrix of the model. In this paper we present the two mentioned methodologies for the D-optimality criteria and we show a result which is useful to find D-optimal designs for heteroscedastic models when the variance of the response is a function of the mean. Then we apply both methods with an example, where the model is nonlinear and the variance is not constant. Finally we find the D-optimal designs with each methodology, calculate the efficiencies and evaluate the goodness of fit of the obtained designs via simulations.

Keywords : D-efficiency; D-optimal design; Box-Cox transformations; \linebreak Heteroscedasticity.

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