Abstract
In techniques for reduction of dimensionality, initially the components of the original vector variable are grouped into several disjoint subsets. New variables with a reduced dimension are then constructed. Often several meaningful alternative groupings can be formed. Optimal choice of the grouping and/or the dimension for the new variables is of considerable importance. Using a generalization (SenGupta, 1983) of canonical variables, this leads naturally to tests under order restrictions for the generalized variances of the generalized canonical variables. By suitable transformations, it is seen that a solution can be given by an appeal to isotonic regression.
Research supported in part by NSF Grant SE 579-13976 and ONR Contract N00014-75-C-0442.
AMS 1980 subject classificatons: Primary 62H15; Secondary 62F05.
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SenGupta, A. (1986). On Tests Under Order Restrictions in Reduction of Dimensionality. In: Dykstra, R., Robertson, T., Wright, F.T. (eds) Advances in Order Restricted Statistical Inference. Lecture Notes in Statistics, vol 37. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9940-7_13
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DOI: https://doi.org/10.1007/978-1-4613-9940-7_13
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