On the Use of Some Classification Quality Measure to Construct Mean Value Estimates Under Nonresponse

Abstract

Several procedures have been developed for estimating the mean value of population characteristic under nonresponse. Usually estimators use available auxiliary information as a basis for the nonresponse correction. Some of them rely on classification procedures which allow to divide the population under study into subsets of units which are similar to sample respondents or sample nonrespondents. This allows to approximate the proportion of respondent and nonrespondent stratum in the population. Nonrespondents are then subsampled and estimates of population parameters are constructed. Such estimators are more accurate than the standard estimator for two-phase sample when distributions of auxiliary variables in respondent and nonrespondent stratum differ significantly. However, in the case when these distributions are similar the improvement disappears and classification-based estimator may be less accurate than the standard one. In this paper another mean value estimator is proposed in order to eliminate this disadvantage. It is constructed as a combination of a standard (unbiased) two-phase estimator and a classification-based estimator. The weights of this combination are functions of some classification quality measure. The proposed mean value estimator should behave like a classification-based estimator when auxiliary characteristics seem to be useful for classification and behave like a standard estimator otherwise. The results of Monte Carlo simulation experiments aimed at assessing the properties of the proposed combined estimator are presented.