Optimal designs for quantile regression models
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Date
2011-08-11
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Abstract
Despite of their importance optimal designs for quantile regression models have not
been developed so far. In this paper we investigate the D-optimal design problem for the location
scale nonlinear quantile regression model. We provide a necessary condition to check for the
optimality of a given design and use it to determine bounds for the number of support points of locally
D-optimal designs. The results are illustrated determining locally, Bayesian and standardized
maximin D-optimal designs for quantile regression analysis in the Michaelis-Menten and EMAX
model, where the location and the scale function are related by a known link function.
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Keywords
EMAX model, heteroscedasticity, locally optimal design, Michaelis-Menten model, quantile regression, robust designs