On Twostage Estimate Based on Independent Estimate of Covariance Matrix

When an independent estimate of covariance matrix is available, we often prefer twostage estimate (TSE). Expressions of exact covariance matrix of the TSE obtained by using all and some covariables in covariance adjustment approach are given, and a necessary and sufficient condition for the TSE to be superior to the least square estimate and related large sample test is also established. Furthermore the TSE, by using some covariables, is expressed as weighted least square estimate. Basing on this fact, a necessary and sufficient condition for the TSE by using some covariables to be superior to the TSE by using all covariables is obtained. These results give us some insight into the selection of covariables in the TSE and its application.