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Prediction and sufficiency in the model factor analysis

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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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en

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application/pdf

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http://eprints.lse.ac.uk/6597/1/Prediction_and_Sufficiency_in_the_Model_Factor_Analysis.pdf

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