Ratio and regression estimation

Abstract

AbstractInexpensive and/or readily available auxiliary variable, x, values may often be available at little or no cost. If these variables are highly correlated with the target variable, y, then use of ratio or regression estimators may greatly reduce sampling variance. These estimators are not unbiased, but bias is generally small compared to the target of estimation and contributes a very small proportion of overall mean square error, the relevant measure of accuracy for biased estimators. Ratio estimation can also be incorporated in the context of stratified designs, again possibly offering a reduction in overall sampling variance. Model-based prediction offers an alternative to the design-based ratio and regression estimators and we present an overview of this approach. In model-based prediction, the y values associated with population units are viewed as realizations of random variables which are assumed to be related to auxiliary variables according to specified models. The realized values of the target variable are known for the sample, but must be predicted using an assumed model dependency on the auxiliary variable for the non-sampled units in the population. Insights from model-based thinking may assist the design-based sampling theorist in selection of an appropriate estimator. Similarly, we show that insights from design-based estimation may improve estimation of uncertainty in model-based mark-recapture estimation.