The First Phase Order Sampling for the Second Phase Stratification

A two-phase sampling design with order sampling in the first phase and stratified simple random sampling in the second phase is studied in the paper. Order sampling is a sampling design with-out replacement and with the elements selected with probabilities proportional to their size. The second-phase stratification using suitably chosen sample sizes in the strata allows us to equalize the design weights for elements. Calculation of the first-phase inclusion probabilities is computationally complicated, therefore the quasi-Horvitz-Thompson estimator of the total is used. Its approximate variance, the estimator of this variance and simulation results are presented