Optimal designs for models under the Flexible Closed Skew Normal Distribution
We introduce a parsimonious and flexible subclass of the Closed Skew Normal (CSN) distribution. We have derived and proved several important properties for this subclass, showing that it is identifiable and closed under marginalization and conditioning, and that zero correlation implies independence. We discuss why these random fields serve as valid models, and we investigate least squares estimators within this framework. In addition, using the Fisher information matrix of a particular parametrization of the model, we show the optimal locations to improve model estimators under the normal distribution. Finally, to assess the potential impact of this optimization process in linear models, we present a comparative simulation study incorporating different levels of bias.
Keywords: Optimal experiment designs Skew Distributions/Responses Fisher Information Matrix D-optimal Spatial Statistics