The Choice of the Parameter Values in a Multivariate Model of a Second Order Surface with Heteroscedastic Error

Gabriele Cantaluppi, Umberto Magagnoli

Risultato della ricerca: Contributo in libroChapter

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.
Lingua originaleEnglish
Titolo della pubblicazione ospiteClassification and Multivariate Analysis for Complex Data Structures
EditorB Fichet, D Piccolo, R Verde, M Vichi
Pagine85-93
Numero di pagine9
DOI
Stato di pubblicazionePubblicato - 2011

Keywords

  • Experimental Design
  • Heteroscedastic Errors
  • Second order surfaces
  • Taguchi Methods

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