Abstract
In this paper we have developed an alternative estimator for the Probability Proportional to Size (PPS) with replacement sampling scheme when certain characteristics under study are positively correlated with the selection probability. An analogue to the well-known superpopulation model for finite population is also suggested, using which, we compare the proposed estimator with Hansen and Hurwitz estimator. Finally, an empirical investigation of the performance of the propose estimator has also been made.
Highlights
Probability Proportional to Size (PPS) sampling is a method of sampling from finite population in which a size measure is available for each population unit before sampling and where the probability of selecting a unit is proportional to size
Let Yi be the value of the study variable ݕon the unit U݅, ݅ = 1,..., N
PPS sampling is expected to be more efficient than SRS sampling if the regression line of y on x passes through the origin. When it is not so, a transformation on the auxiliary variable can be made so that the PPS sampling with modified sizes becomes more efficient
Summary
Probability Proportional to Size (PPS) sampling is a method of sampling from finite population in which a size measure is available for each population unit before sampling and where the probability of selecting a unit is proportional to size. In practice we wish to estimate the population total Y = Σyi from the ݕvalues of the units drawn in a sample (u1, u2,..., un) with maximum precision. Hansen and Hurwitz (1943) proposed the idea of sampling with Probability Proportional to Size (PPS) with replacement for positive correlated characteristics. When it is not so, a transformation on the auxiliary variable can be made so that the PPS sampling with modified sizes becomes more efficient.
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