The asymptotic distributions of some estimators for a factor analysis model (Q1822428)

Suppose a set of observable p-dimensional random vectors \(Z_ t\) is related to a set of unobservable k-dimensional factor vectors \(x_ t\) by \[ Z_ t=(\beta_ 0,0)+x_ t(\beta,I)+(e_ t,\mu_ t) \] where \(\beta\) is a \(k\times r\) matrix, \((e_ t,\mu_ t)\) are the residuals, and \(r=p-k\). The limiting distribution of the estimators of \(\beta\), and the covariance matrix of x as well as the covariance matrix of the residuals, are investigated. Under a wide range of assumptions about the true factors an explicit expression is obtained. The forms of the theorem are computationally efficient. A program to compute the covariance matrix is developed by the authors.