Evaluation of probability proportional to predictions estimators of total stem volume

Abstract

A plethora of probability proportional to predictions (PPP) estimators makes it hard for a user to decide which one to use. This study demonstrates the need for an extensive screening procedure by example of four PPP estimators of total stem volume and five estimators of sampling error. Bias, absolute bias, root mean square error, sample-based estimators of sampling error, and achieved significance levels of confidence intervals with a nominal significance level were compared across 832 distinct settings. Population size, sample size, the variance and skewness of the volume predictors, and the strength of the correlation and the slope between predicted and actual stem volume varied between settings. Estimators converged in performance as sample sizes increased but were otherwise sensitive to actual settings. Of the tested estimators, Brewer's "cosmetically calibrated" estimator was consistently the best in terms of mean absolute relative bias and generally favored in an overall assessment of five performance criteria. Grosenbaugh's adjusted estimator was a close second and was often ranked first in overall performance when n > 0.15N.