EXACT AND APPROXIMATE DISTRIBUTIONS OF THE MAXIMUM-LIKELIHOOD ESTIMATE IN A SIMPLE FACTOR-ANALYSIS MODEL

We study a factor analysis model with two normally distributed observa tions and one factor, In the case when the errors have equal variance, the maximum likelihood estimate of the factor loading is given in clo sed form, Exact and approximate distributions of the maximum likelihoo d estimate are considered. The exact distribution function is given in a complex form that involves the incomplete Beta function, Approximat ions to the distribution function are given for the cases of large sam ple sizes and small error variances, The accuracy of the approximation s is discussed.