The group balanced repeated replication (GBRR) method is used in stratified sampling for variance estimation. This method is applied in stratified adaptive cluster sampling when ignores crossover between strata. The another one method is repeatedly GBRR, which involves independently repeating the random grouping T times and then taking the average of the resulting T of GBRR variance estimators. The network sample in each stratum is divided at random into two groups and then the group balanced repeated replication method is applied to the groups. The modified plus estimator in stratified adaptive cluster sampling is studied and compared with the group balanced repeated replication (GBRR) method for variance estimation by simulation study.
Keywords: Group balanced repeated replication; Stratified sampling; Adaptive cluster sampling; Plus estimator
[...] The variance of the estimate variance by RGBRR method is less than the variance of the estimate variance by GBRR about to 10% when nh is more than Conclusions The group balanced repeated replication (GBRR) variance estimator randomly to assign a sample into 2 groups within each stratum and selects balanced replications from the group. The GBRR method and RGBRR method are applied in stratified adaptive cluster sampling. These methods are useful for computing when the variance estimation is difficult to compute. [...]
[...] ˆ+ An unbiased easy-to-compute estimator of the variance of τst _ DT is given by V ( ˆ+ τst _ DT ) 2 N ( N n ) nh ˆ τh h h h ˆ ˆ+ w hi N τst τst _ DT h h n h ( n h i L ( ) ˆ+ The form of an unbiased estimator of the variance of τst _ DT is difficult to compute so the group balanced repeated replication (GBRR) method is very useful for computing the variance estimation in stratified adaptive cluster sampling whereas the estimator of the population total is the same of modified plus estimator. [...]
[...] Thesis, The Pennsylvania State University. Dryver, A.L., and Thompson, S.K. (2005). Improved unbiased estimators in adaptive cluster sampling: Journal of the Royal Statistical Society, Ser.B 157-166. Kish, L., and Frankel, M.R. (1970). Balanced Repeated Replication in Standard Error: Journal of the American Statistical Association 65, 1071-1094. Rao, J.N.K. and Shao, J.(1996). On Balanced Half-Sample Variance Estimation in stratified Random Sampling: Journal of the American [...]
[...] VGBRR τst ( ) ˆ ˆ+ and VRGBRR τst ( ) are the estimate variance by the group balanced repeated replication method from and respectively, and ˆ+ ˆ+ MSE τst _ DT = V τst _ DT ( ) ( ) is an unbiased variance estimator of the modified plus estimator. The formula of coefficient of variation of the variance estimator is ˆ ˆ+ ˆ+ VGBRR τst i MSE τst _ DT i ˆ+ MSE τst _ DT ( CVGBRR ( ) ( ( ) 2 , and CVRGBRR ˆ ˆ+ ˆ+ VRGBRR τst i MSE τst _ DT i ˆ+ MSE τst _ DT ( ( ) ( ( ) 2 , where ˆ+ MSE τst _ DT = ( ) + ˆ τst _ DT i ) i y ) Table 1 Relative bias of variance and coefficient of variation by GBRR method nh MSE ( ˆ+ τst _ DT ) ˆ ˆ+ VGBRR τst _ DT ( Group Balanced Repeated Replication (GBRR) ) RBGBRR CVGBRR - 0.046 - Table 2 Relative bias of variance and coefficient of variation by RGBRR method nh MSE ( ˆ+ τst _ DT ) ˆ ˆ+ VRGBRR τst _ DT ( ) Repeatedly GBRR T = 20 RBRGBRR CVRGBRR - 0.045 - From Table 1 and Table it can be seen that the RBGBRR and RBRGBRR are less than seven percent points; that is, ˆ ˆ ˆ+ ˆ+ ˆ+ VGBRR τst _ DT and VRGBRR τst _ DT are close to the MSE τst _ DT . [...]
[...] be the total of y-values in the network i with stratum h m hi be the number of the units in the network i with stratum h The unbiased estimator of the population total is ˆ ˆ τst = τh h L L = Nh nh w hi h n h i A modified plus estimator (based on Dryver and Thompson, 2005) based on Hansen-Hurwitz estimator by applying the Rao-Blackwell theorem are as follows. The final sample s = s h can be partitioned into two parts. [...]
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