An optimal property of principal components
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 oplmciiity and regress ion optimality. The first three optimality properties can be found in Okamota (1969) and the last one can be found in Obenrhain (1972). In this paper we present a new regression optimality of sample principal components.