Statistical Inference in Factor Analysis
COLUMBIA UNIVERSITY New York City United States
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In this paper we discuss some methods of factor analysis. The entire discussion is centeredaround one general probability model. We consider some mathematical problemsof the model, such as whether certain kinds of observed data determine the model uniquely.We treat the statistical problems of estimation and tests of certain hypotheses. Forthese purposes the asymptotic distribution theory of some statistics is treated.The primary aim of this paper is to give a unified exposition of this part of factor analysisfrom the viewpoint of the mathematical statistician. The literature on factor analysisis scattered moreover, the many papers and books have been written from many differentpoints of view. By confining ourselves to one model and by emphasizing statisticalinferences for this model we hope to present a clear picture to the statistician.The development given here is expected to point up features of model-building andstatistical inference that occur in other areas where statistical theories are being developed.For example, nearly all of the problems met in factor analysis are met in latentstructure analysis.
- Statistics and Probability