Stepwise estimators for three-phase sampling of categorical variables

Three-phase sampling can be a very effective design for the estimation of regional and national forest cover type frequencies. Simultaneous estimation of frequencies and sampling variances require estimation of a large number of parameters; often so many that consistency and robustness of results becomes an issue. A new stepwise estimation model, in which bias in phase one and two is corrected sequentially instead of simultaneously, requires fewer parameters. Simulated three-phase sampling tested the new model with 144 settings of sample sizes, the number of classes and classification accuracy. Relative mean absolute deviations and root mean square errors were, in most cases, about 8% lower with the stepwise method than with a simultaneous approach. Differences were a function of design parameters. Average expected relative root mean square errors, derived from the assumption of a Dirichlet distribution of cover-type frequencies, tracked the empirical root mean square errors obtained from repeated sampling with - 10%. Resampling results indicate that the relative bias of the most frequent cover types was slightly inflated by the stepwise method. For the least common cover type, the simultaneous method produced the largest relative bias.