Large-sample theory for the linear structural relation

Abstract

The sampling properties of estimators of the structural parameters in a linear structural relationship are studied, using the usual error-in-variables model. Under various assumptions about the error variances, large-sample variances, covariances and biases are found. The results depend critically on the sequences { n −1 σ x 2 i and { n −1 σ x 2 i }, where { x i are the true x -values, and when these can be regarded as sampled from some distribution with finite mean and variance these sequences will converge in probability to their population values, which may be estimated without precise specification of the x -distribution