Abstract
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.
Highlights
In sampling, the sampling units, as usually defined, are similar in size and structure
The total sample size can be subject to unduly large variation if it is based on random selection of clusters that differ greatly in size
They suggested another alternative estimator of the population total for probability proportional to size with replacement sampling scheme which considers the rough value of the correlation coefficient between the study variable y, and the ancillary variable x
Summary
The sampling units, as usually defined, are similar in size and structure. Bansal and Singh (1985) put forward another alternative estimator of the population total for characteristics that are poorly correlated with the selection probabilities They suggested another alternative estimator of the population total for probability proportional to size with replacement sampling scheme which considers the rough value of the correlation coefficient between the study variable y, and the ancillary variable x. Their action (suggesting another alternative estimator) is informed by the fact that the situation considered in the model in Rao (1966) is “not commonly encountered in practice, since hardly can the correlation in the population be exactly equal to zero”.
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