Inference based on regression estimator in double sampling

The problem of hypothesis testing using the regression estimator in double sampling is considered. Test procedures are provided when the covariance matrix between the primary and the auxiliary variables is either partially known or completely unknown. For the latter case a new 'studentized' version of the regression estimator is proposed as a test statistic. The exact null distribution of this statistic is derived in a special case. An approximation to the null distribution is derived in the general case and studied by means of the Monte Carlo method. The problem of choosing between the double sample regression estimator and the single sample mean estimator is also discussed.