The paper describes an experimental procedure to choose the values for a multivariate vector x, under these conditions: average of Y(x) equal to a target value and least variance of Y(x), linked to x by a 2nd order model, with a heteroschedastic error. The procedure consists of two steps. In the first step an experimental design (we consider a three level full factorial design, for simplicity) is performed in the feasible space X of the control factors to estimate the parameters characterizing the response surface of the mean. Then a second experimental design is performed on a target set A, subset of X satisfying the condition on the average of Y(x). This second step determines the choice of x using a classification criterion based on the ordering of the sample mean squared errors. In both steps the model parameters are estimated by an iterative method.
Magagnoli, U., Cantaluppi, G., The Choice of the Parameter Values in a Multivariate Model of a Second Order Surface with Heteroschedastic Error, in First joint meeting of the Société Francophone de Classification and the Classification and Data Analysis Group of the Italian Statistical Society, Book of Short Papers, (Caserta, 11-13 June 2008), Edizioni Scientifiche Italiane, Caserta 2008: 369-372 [http://hdl.handle.net/10807/24270]
The Choice of the Parameter Values in a Multivariate Model of a Second Order Surface with Heteroschedastic Error
Magagnoli, Umberto;Cantaluppi, Gabriele
2008
Abstract
The paper describes an experimental procedure to choose the values for a multivariate vector x, under these conditions: average of Y(x) equal to a target value and least variance of Y(x), linked to x by a 2nd order model, with a heteroschedastic error. The procedure consists of two steps. In the first step an experimental design (we consider a three level full factorial design, for simplicity) is performed in the feasible space X of the control factors to estimate the parameters characterizing the response surface of the mean. Then a second experimental design is performed on a target set A, subset of X satisfying the condition on the average of Y(x). This second step determines the choice of x using a classification criterion based on the ordering of the sample mean squared errors. In both steps the model parameters are estimated by an iterative method.
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