A New System of Inclusion Probability Proportional to Size Sampling Schemes of Two Units

Abstract

Background: One of the well-liked varying probability sampling methods is an inclusion probability proportional to size sampling scheme in which the first order inclusion probabilities are exactly proportional to size measures. Such schemes for sample size two have attracted attention of survey statisticians because of their simplicity in implementation, and nonnegative, unbiased and stable variance estimation of the Horvitz-Thompson estimator.

Objective: The purpose of the paper is to set forth a system or family of inclusion probability proportional to size sampling schemes of two units for estimating a finite population total.

Materials and Methods: Standard sampling techniques have been used to examine basic properties of the proposed family of sampling schemes as desired under Horvitz-Thompson framework. A numerical study, utilizing live data of 21 populations, has been conducted to evaluate relative performance of some member schemes of the family.    

Results: The suggested family has been shown to satisfy almost all basic requirements of an inclusion probability proportional to size design and have flexible feature as it easily reduces to some of such existing designs. Three new designs, as special cases of the proposed family, have also been explored. Empirical results show that one of the new schemes comes out as the most efficient and the most stable among the comparable schemes.  

Conclusion: Versatility property of the suggested system of sampling schemes along with fulfilment of fundamental needs of an inclusion probability proportional to size scheme will encourage for further research to detect other schemes of the system or outside the system with greater accuracy.