Exploratory factor analysis-Parameter estimation and scores prediction with high-dimensional data

In an approach aiming at high-dimensional situations, we first introduce a distribution-free approach to parameter estimation in the standard random factor model, that is shown to lead to the same estimating equations as maximum likelihood estimation under normality. The derivation is considerably simpler, and works equally well in the case of more variables than observations (p>n). We next concentrate on the latter case and show results of type: • Albeit factor loadings and specific variances cannot be precisely estimated unless n is large, this is not needed for the factor scores to be precise, but only that p is large; • A classical fixed point iteration method can be expected to converge safely and rapidly, provided p is large. A microarray data set, with p=2000 and n=22, is used to illustrate this theoretical result