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Multivariate calibration involves the use of an estimated relationship between a multivariate response vector Y and an explanatory vector X to predict unknown X in future from further observed responses. With modern instrumentation the dimension of the response vector may be very large (of the order 1000) and yet the number of observations small. Under such circumstances standard approaches to calibration give rise to non-unique predictors of future X. To obtain a unique estimator it is necessary to impose additional structure. We investigate various approaches to dimension reduction to do this. Areas of application are the food and chemical industries
Denham et al. (1993) studied this question.