Performance of empirical predictors in two-stage cluster sampling

To evaluate the performance of the empirical predictors presented in San Martino et al. (2005), we compute the cases where they are the best, “equivalent” to the best (tables 1) or poor (table2). We consider only the case of equal unknown within cluster variances. First, we consider the cases in which each of the proposed predictors has the best performance, i.e. we compute the percentage of cases where each predictor has minimum EMSE. These percentages are calculated considering the combination of all intra-class correlations and unit sampling fractions in the denominator, i.e., 168 for the population with N=10 and M=5 and 392 for the others (labelled , , s t f ρ ρ ∀ in the following tables). As these percentages may be inflated or understated because we are considering various “extreme” intra-class correlation coefficients (0.01/0.05, 0.095/0.99/1) in comparison with the other values (0.2, 0.5, 0.8), they were recomputed after elimination of the values 0.01 and 0.99. In this case ,we use 90 in the denominator for the population with N=10 and M=5 and 210 for the others (labelled “Excluding , s t ρ ρ = 0.01,0.99” in the tables below). In some cases, the percentages exceed 100% (marked with *), because the EMSE for the SS and RP model predictors have exactly the same minimum value. In the paper, to determine equivalence between predictors, we computed the RPI (relative percent increase) in EMSE for each model predictor relatively to that of the RP model predictor. When variances are known, this is a good criterion because the RP model predictor is always the best. When variances are unknown, the RP model predictor is not always the best, so a better criterion would be to determine the RPI in EMSE for each model predictor relatively to the best predictor (i.e., that with minimum EMSE). We computed the percentage of cases where each predictor may be considered equivalent to the best one (0 < RPI < 15% or, equivalently, 1.15 predictor best predictor EMSE EMSE < ), using the same criterion previously considered to compute