The Distribution of FIML in the Leading Case
证明在完全不可识别情形下，全信息最大似然估计量的分布是多元柯西分布，对理解结构方程估计量的性质有帮助。
In a recent article (1984a) Phillips showed that the distribution of the limited information maximum likelihood (LIML) estimator of the coefficients of the endogenous variables in a single structural equation is multivariate Cauchy in the leading (totally unidentified) case. The purpose of the present note is to show that the same result holds for the full information maximum likelihood (FIML) estimator. Our proof relies on the theory of invariant measures on a Stiefel manifold. This approach provides a major simplification of the derivation of the LIML result given in the earlier article and extends to the FIML case without difficulty. We start by illustrating its use for LIML.(This abstract was borrowed from another version of this item.)