Self-Critical, and Robust, Procedures for the Analysis of Multivariate Normal Data.

摘要

A procecure for performing sensitivity analysis of data vis-a-vis the multivariate error model, with or without structural variables, is proposed. It is based on an estimation procedure, a generalization of maximum likelihood, which is indexed on a user-specified value c. The sensitivity analysis proceeds in the following way: the parameters of a set of data presumed to follow a multivariate normal error model are estimated via maximum likelihood (c = 0). The parameters are next estimated for an index c1 > 0. The sensitvity in parameter estimates is noted. The parameters are next estimated for a user-specified index c2 >= c1 > 0 and the sensitivity of the parameter estimates to the change in c is again noted. This process may have one or more values of c > 0. If the parameter estimates are sensitive functions of c, the model and the data are not mutually consistent and both require further detailed study. The items of data which are most contributory to this sensitivity are identified by an examination of observational weights which are a byproduct of the analysis. If the parameters and observational weights are non-sensitive to changes in the index c, then one can generally be confident of the internal consistency of the data and the error model. Fixed values of the index c provide roubust estimation procedures for model parameters. Asymptotic relative efficiencies and influence functions are provided for fixed values of c. The results of a small Monte Carlo study suggest that the asymptotic properties of the estimators are rapidly attined. Several illustrations are given. (Author)