%0 Research article
%T Comparison of randomized branch sampling with and without replacement at the first stage
%A Cancino, Jorge
%A Saborowski, Joachim
%D 2005
%J Silva Fennica
%V 39
%N 2
%R doi:10.14214/sf.384
%U https://silvafennica.fi/article/384
%X Randomized Branch Sampling (RBS) is a multistage sampling procedure  using natural branching in order to select samples for the estimation of  tree characteristics. Usually, sampling units are selected with unequal  probabilities. Conventional RBS uses sampling with replacement (SWR)  for repeated sampling on the first stage, and the sample size equals 1  on all subsequent stages, thus resulting in n so-called sample paths.  When the sampling fraction is large multiple selections of first stage  units are likely. Sampling without replacement (SWOR) at the first stage  is an alternative that is expected to increase efficiency of the  procedure. In this case, the second stage sample size m must be larger  than 1 to enable unbiased variance estimation. In the present study, a  theoretical and an empirical comparison of the conventional RBS and the  SWOR variant was accomplished. Requiring a certain precision of the RBS  estimation, the conventional RBS method is mostly more time-consuming  than the variant with SWOR at the first stage. Only if m = 1 is chosen  as second stage sample size for the SWOR RBS, this is often more  time-consuming. In those cases, conventional RBS is up to 5% cheaper. In  general, the larger m is, the more expensive is conventional RBS  compared with the variant with swor at the first stage. The smaller the  ratio of the variance between the primary units to the total variance of  the estimate, the larger is the advantage of the SWOR variant.  Generally, it can be shown that the gain of efficiency by SWOR is larger  in case of weak correlations between auxiliary and target variable.