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Title: Experimental designs to test for heteroscedasticity in a regression model Authors:  Chiara Tommasi - University of Milan (Italy)
Alessandro Lanteri - University of Milan (Italy) [presenting]
Jesus Lopez-Fidalgo - University of Navarra (Spain)
Samantha Leorato - University of Milan (Italy)
Abstract: The goal is to design an experiment to detect a specific kind of heteroscedasticity in a non-linear Gaussian regression model. To test the homoscedastic case (under the null hypothesis) against local alternatives, a likelihood-based test is usually applied. Suitable design criteria for this task are Ds- and KL-criteria because they are related to the noncentrality parameter of the asymptotic chi-squared distribution of a likelihood-based test. Thus, they maximize the asymptotic power of the test. Specifically, when the variance function depends just on one parameter, these criteria coincide asymptotically, and in particular, the D1-criterion is proportional to the noncentrality parameter. Differently, when the variance function depends on a vector of parameters, the two criteria are not asymptotically equivalent anymore; the KL-optimum design outperforms the Ds-optimal design because it converges to the design that maximizes the noncentrality parameter. A simulation study, concerning the computation of asymptotic and exact powers of the log-likelihood ratio statistic, confirms these theoretical results.