On best affine prediction |
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Authors: | Heinz Neudecker Albert Satorra |
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Affiliation: | (1) Cesaro, Oosterstraat 13, 1741 GH Schagen, The Netherlands;(2) Department of Economics and Business, Universitat Pompeu Fabra, Ramon Trias Fargas 25-27, 08005 Barcelona, Spain |
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Abstract: | The theory of best affine prediction (BAP) is extended to the vector case with possibly singular variance matrix of the predictor variable. The theory is then applied to derive Thomson’s classical predictor for factor scores, allowing for a singular variance matrix of the factors. The results are formulated in a free distribution setting. Further, Bartlett’s estimator is considered and compared with Thomson’s predictor. The authors are thankful to the two referees, one for a suggestion that led to the Addendum of the paper, and the other one for several very useful remarks. Research supported by the Spanish grant BEC2000-0983. |
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Keywords: | factor analysis factor scores optimal prediction mean-squared error singular matrices Moore-Penrose inverse |
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