Robustness criteria, determination

The first step of Croux and Ruiz-Gazen making PCA more robust is centering the data with a robust criterion, the LI-median, that is, the point which minimizes the sum of Euclidean distances to all points of the data. In a next step, directions in the data space, which are not influenced by outliers, are determined by maximizing a robust parameter, the estimator. To calculate this estimator, first all objects are projected onto normalized vectors passing through each point and the LI-median center. Then for each projection, the Qn, that is, the first quartile of all pairwise differences, is calculated as follows ... 

The importance of this result is that it leads to an overall objective criterion for sample size determination that averages criteria based on specific model assumptions. Thus it provides a solution that is robust to model uncertainty. Closed-form calculations of (8) are intractable, so we have developed numerical approximations to the conditional entropies Ent(6k n, yk, MLk) and Ent(9k n, yk, MGk). The computations of the expected Bayes risk are performed via stochastic simulations and the exact objective function is estimated by curve fitting as suggested by Miiller and Parmigiani (1995). These details are available on request from the authors. 

Robustness of the identification procedure Experimental difficulties caused by the determination of the mechanical parameters involved in the identification procedure User-friendliness of the yield criterion Acceptance of the yield criterion in the scien-tificAndustrial community... 

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