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Using as a starting point the
hypothesis of normality of X|(Y=y), we developed a methodology for dimension
reduction for the forward regression of Y|X under the sufficient dimension reduction
paradigm. This methodology includes
finding the dimension of the central subspace, maximum likelihood estimation
for a basis of the central subspace, testing for predictors and prediction.
In order to develop
this methodology necessary and sufficient conditions for each method are
studied. After that, maximum
likelihood estimators for the parameters are found. This allows us to develop inference
procedures that are shown to work in simulation studies. Finally, the models are applied to get
conclusions in real data set examples.