ASYMPTOTIC CONFIDENCE REGIONS FOR A LINEAR STRUCTURAL RELATIONSHIP

Abstract

For the problem of finding a confidence region for the linear structural relation, Brown's method, which assumes that the error variances are known, is shown to be applicable to the case when the error variances are unknown but equal. A new method is presented for obtaining first an asymptotic confidence region for the unknown coefficient vector based on the asymptotic distribution of the maximum likelihood estimator and then one for the structural hyperplane. Numerical computation in the bivariate case shows that our confidence region for the structural line is contained in Brown's region (modified in the above sense) with the same confidence level.