An empirical evaluation of the accuracy of the Hartley and Rao (1962) variance approximation following PPS systematic sampling

Hartley and rao (1962) formalized a strategy of unequal probability systematic sampling combined with the horvitz-thompson estimator of the population total. they also provided an expression for the variance of the estimator based on a large population cum sample approximation to the joint inclusion probabilities. likewise they offered an estimator of this variance. to our knowledge there is limited evidence regarding the effectiveness of these asymptotic results to sampling from small populations. based upon simulated sampling from two populations,neither of which are regarded as very large,the performance of both the variance approximation and estimator of same were examined. both were found to be quite accurate. © 2011 pakistan journal of statistics.