@inbook{97cca8495eb44e99b0f7a0b47bc16dbd,
title = "The Choice of the Parameter Values in a Multivariate Model of a Second Order Surface with Heteroscedastic Error",
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.",
keywords = "Experimental Design, Heteroscedastic Errors, Second order surfaces, Taguchi Methods, Experimental Design, Heteroscedastic Errors, Second order surfaces, Taguchi Methods",
author = "Umberto Magagnoli and Gabriele Cantaluppi",
year = "2011",
doi = "10.1007/978-3-642-13312-1_8",
language = "English",
isbn = "978-3-642-13311-4",
series = "STUDIES IN CLASSIFICATION, DATA ANALYSIS, AND KNOWLEDGE ORGANIZATION",
pages = "85--93",
editor = "B Fichet and D Piccolo and R Verde and M Vichi",
booktitle = "Classification and Multivariate Analysis for Complex Data Structures",
}