On the problems of PPS sampling in multi-character surveys
This paper, which is on the problems of PPS sampling in multi-character surveys, compares the efficiency of some estimators used in PPSWR sampling for multiple characteristics. From a superpopulation model, we computed the expected variances of the different estimators for each of the first two finite populations considered, as well as the exact bias and variance of each of these estimators. The results obtained show that the estimators proposed by Rao (1966), Amahia et. al. (1989) and the alternative in Amahia et. al. (1989) are better than the conventional estimator. In population I, where the study variable and the ancillary variable are highly and positively correlated, results show that the estimator in Amahia et. al. (1989) fare better than the alternative estimator. On the other hand, the results obtained from our population II where the correlation between the study variable and the ancillary variable is poor, reveal that the alternative estimator in Amahia et. al. (1989) is more efficient. Several other finite populations whose ρare neither too high as in population I nor too poor as in population II were considered and it was discovered that the competition for efficiency only rests with the two estimators suggested by Amahia et al (1989) and Rao (1966). These interesting comparative results are shown in Tables.