Optimal control designs using predicting densities for the multivariate linear model |
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Authors: | Tim K. Peps Martin S. Levy |
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Affiliation: | 1. Statistician , General Electric Company , Corporate Research and Development One Research Circle, Schenectady, NY, 12301;2. Associate Professor Departmetn of Quantitative Analysis and Operations Mangement , University of Cincinnati , Cincinnati, OH, 45221-0130 |
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Abstract: | We provide an application of a variety of predicting densities to quality control involving multivariate normal linear models. We produce optimal control designs for single muleivaiiate future observations using predicting densities employing estimative, profile likelihood, Hinkley-Lauritzen, Butler, Bayesian, and Parametric Bootstrap methodologies. The decision-theoretic optimality criterion is an intuitively appealing quadratic consumer-producer risk function. The optimal control design arising from an optimal Kullback-Leibler frequentist prediction density is shown to coincide with that arising from an optimal Kullback-Leibler Bayesian predictive density. An example involving EVOP is provided to illustrate the methodology and to raise questions concerning the relative merics of the variety of predictive approaches in the quality control context. |
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Keywords: | Predictive inference Bayesian Predictive Density Kullback-Leibler Divergence Future Risk Quality Control |
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