Leveraging the Rao–Blackwell theorem to improve ratio estimators in adaptive cluster sampling

Abstract

Rao-Blackwellization is used to improve the unbiased Hansen-Hurwitz and Horvitz-Thompson unbiased estimators in Adaptive Cluster Sampling by finding the conditional expected value of the original unbiased estimators given the sufficient or minimal sufficient statistic. In principle, the same idea can be used to find better ratio estimators, however, the calculation of taking all the possible combinations into account can be extremely tedious in practice. The simplified analytical forms of such ratio estimators are not currently available. For practical interest, several improved ratio estimators in Adaptive Cluster Sampling are proposed in this article. The proposed ratio estimators are not the real Rao-Blackwellized versions of the original ones but make use of the Rao-Blackwellized univariate estimators. How to calculate the proposed estimators is illustrated, and their performance are evaluated by both of the Bivariate Poisson clustered process and a real data. The simulation result indicates that the proposed improved ratio estimators are able to provide considerably advantageous estimation results over the original ones.

Generalized Robust Regression techniques and adaptive cluster sampling for efficient estimation of population mean in case of Rare and Clustered Populations

“…The pioneer researcher who conceptualized the ACS was Thompson (1990) and have also proposed the various unbiased estimators. Various researchers have put their valuable efforts to enhance the proficiency of mean or variance estimation by incorporating the ancillary information either using single auxiliary or bivariate auxiliary variable in different sampling designs for details see Thompson (1991), Alomari and Shahzad (2023), Chao (2004) 2020) under SRS and stratified sampling schemes. However, no study is available on the use of robust regression in mean estimation under ACS.…”

“…. The values of ( ) u v, can be found in Table [6] and Table [7]. For more comprehensive information, refer to Yasmeen and Thompson (2020).…”

Estimation of General Parameter Under Stratified Adaptive Cluster Sampling Based on Dual Use of Auxiliary Information

“…Data of teals from Smith et al [32] are considered for numerical comparison of existing and proposed estimators. The data on Blue-winged teal is used as study variable for stratum 1 and data on Greenwinged teal is used as study variable for stratum 2 and auxiliary variables (x h and z h ) are generated using the concept given by Dryver and Chao [33] and Chao et al [34] as…”

Adaptive cluster sampling for negatively correlated data

“…Chao et al. () and Lin and Chao () further improved the ratio estimators under ACS by making use of the Rao–Blackwell theorem.…”

“…Dryver and Chao (2007) proposed another ratio estimator under ACS based on the modified Hansen-Hurwitz (HH) estimator. Chao et al (2011) and Lin and Chao (2014) further improved the ratio estimators under ACS by making use of the Rao-Blackwell theorem.…”