The estimation of binary responses in factor analysis models is often complicated, because the marginal likelihood involves an intractable integral. When the number of latent variables is large, the dimensionality of a required integral will be high, and thus numerical integration would not be...

The normal distribution based likelihood ratio (LR) statistic is widely used in structural equation modeling. Under a sequence of local alternative hypotheses, this statistic has been shown to asymptotically follow a noncentral chi-square distribution. In practice, the population mean vector and...

Three types of characterizations for two subclasses of spherical distributions are presented. Within the class of spherical distributions, we prove that the symmetric Kotz-type distributions (under some restricted parameters) and the symmetric Pearson-type II distributions are characterized by...