Various optimality properties of principal components of a sample as well as of a random vector have been presented by several authors (Anderson, 1958; Darroch, 1965; Kshirsagar, 1972; Obenchain, 1972; Okamoto and Kanazawa, 1968; Okamoto, 1969). Generally speaking, they can be classified into four categories: variation optimality, information loss optimality, correlation optimality and regression optimality. The first three optimality properties can be found in Okamoto (1969) and the last one can be found in Obenchain (1972). In this paper we present a new regression optimality of sample principal components.
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