Abul Naga, Ramses H. (1997) Prediction and sufficiency in the model factor analysis. DARP, 31. Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science, London, UK.
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We contrast two approaches to the prediction of latent variables in the model of factor analysis. The likelihood statistic is a sufficient statistic for the unobservables when sampling arises from the exponential family of distributions. Linear predictors, on the other hand, can be obtained as distribution-free statistics. We provide conditions under which a class of linear predictors is sufficient for the exponential family of distributions. We also examine various predictors in the light of the following criteria: (I) sufficiency, (ii) mean-square error, and (iii) unbiasedness and illustrate our results with the help of Chinese data on living standards.
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