PPS and Random Sampling Estimation Using some Regression and Ratio Estimators for Underlying Linear and Curvilinear Models

Abstract

Abstract Two thousand samples of 30 units were drawn from selected populations for which linear or curvilinear underlying models were postulated between the variable of interest and a covariate. Ratio, and linear and nonlinear regression estimators were compared for bias and relative efficiency of the estimates generated. Regression estimators were found to be the most precise estimators of totals for both random and probability proportional to size (PPS) sampling for a series of tree populations for samples of size 30. The weighted regression estimator in PPS sampling was consistently more efficient than the standard Horvitz-Thompson estimator. For the populations studied, the nonlinear and polynomial regression estimators were not efficient except in very specific cases, probably due to the absence of clear nonlinear trends in most of the populations. (Such nonlinear or curvilinear models do exist in specific stands for certain variables.) The quadratic polynomial regression estimator had the smallest variance in the case where a clear nonlinear relationship existed in the population for the variable pair considered. A general nonlinear regression estimator was inefficient for a population with a nonlinear relationship. Generally, estimation bias was small and coverage probabilities (containing the parameter of interest) were high for all estimators and populations. Jackknife variance estimates were not consistently better than the classical variance estimates of the true variances for any of the estimators. For. Sci. 33(4):997-1009.