多项Probit模型参数的极大似然估计

Maximum Likelihood Estimates of Parameters in Multinomial Probit Model

本文考虑多项probit模型中参数的极大似然估计(MLE)的存在性.在协方差阵已知和均匀结构两种情况下,给出MLE存在的充要条件.

The multinomial probit (MNP) model has been widely used in biometrics,econometrics and transportation modeling.This model can accommodate arbitrarily complicated relationships among the probabilities of the vairous categories quite naturally.However,despite potential broad applications,its usage has been limited by the compulational burden associated with estimating the parameters.This paper mainly examines necessary and sufficient conditions for the existence of Maximum Likelihood Estimation (MLE) for MNP model.Albert and Anderson (1981) gave separation and overlap conditions for the existence of the MLE in logistic models.We generalize their conditions to MNP model,giving necessary and sufficient conditions for the existence of a finite MLE when covariance matrix is known or it has a special structure uniform structure.