Bias and Efficiency of the Consistent Weighted Regression Estimators in Finite Population Sampling

摘要

The leading terms of the bias of the ratio and regression estimators are known to be of order n to the minus 1 power. We use a finite population decomposition to give a different expression for the leading term of the bias. Fitting a regression line to the finite population, we show that the intercept of the regression line causes the bias of the ratio estimator. Fitting a quadratic regression to the finite population, we show that the bias of the regression estimator is caused by the quadratic term. We also give a compact and intuitive formula for the leading term of the bias of the weighted regression estimators for p-auxiliary variables. Using the same decomposition, we can rewrite the variance formula of some popular estimators in terms of some simple and interpretable population characteristics. We prove that under simple random sampling scheme the unweighted regression estimator is the most efficient estimator. The extension for the p-auxiliary variates is also given.