On Estimating the Variance in Sampling with Probability Proportional to Aggregate Size
Abstract The problem of estimating the variance of the ratio estimator in sampling with probability proportional to aggregate size is investigated. The form of nonnegative unbiased variance estimators is found. For sample size n = 2, it is shown that there is at most one nonnegative unbiased variance estimator, whereas for n > 2, two different, possibly nonnegative, unbiased variance estimators are proposed. The performance of the proposed unbiased variance estimators, as regards their stabilities and probabilities of getting a negative value, is empirically investigated employing a variety of real populations.