Small Domain Estimation: A Conditional Analysis

原文摘要

In estimating means, totals, and other parameters for small domains of a finite population, the survey statistician is usually faced with a domain sample size that is random rather than controlled at the selection stage. Often a sensible approach is to make design-based inference conditionally on the realized sample size in the domain (nd ). In this article, we suggest and analyze some small domain estimators and their design-based conditional confidence intervals. The conditional outlook leads us to some new small domain estimators that (a) are based on regression of pertinent auxiliary information and are therefore efficient to the extent that the auxiliary information is strong; (b) are nearly design unbiased, conditionally on nd , as well as unconditionally; and (c) give rise to design-based confidence intervals that are valid conditionally as well as unconditionally. The conditional properties of these new regression estimators are first derived theoretically, then confirmed through a Monte Carlo simulation based on Canadian business survey data. The well-known synthetic estimator has the attractive stability property that the variance is often very small, but it is avoided by many survey statisticians owing to the possibility of a substantial design bias. Several “improved” methods aim at reduced bias yet good stability by building the estimator as the sum of a synthetic estimator term and an “adjustment term.” In particular, the adjustment term can be made to eliminate the bias almost completely, as in the regression estimation method of Särndal (1981, 1984). However, such a bias-removing adjustment term adds a considerable variance component when the domain sample size nd is very small. This is viewed as the price to pay for “measurability”—that is, being able to calculate, from the sample itself, an estimate of the sampling error and a valid confidence interval. In this article we construct a new regression estimator in which the adjustment term is “dampened” for particularly small nd . This approach trades a mild bias for a decreased variance and effectively removes the likelihood of “wild” estimates while still admitting a valid design-based confidence interval. It is recommended for practitioners who wish to be able to calculate design-based precision in the form of a valid confidence interval. In our Monte Carlo study, we compare our approach to other methods, including another “synthetic term plus adjustment term method” suggested by Fuller and Harter (1987), in which the emphasis is on obtaining good mean squared error performance, rather than on nearly complete bias removal through the adjustment term. The efficiency gains realized by the latter method over our dampened regression estimator method were not substantial in our Monte Carlo study.

摘要来源：OpenAlex 索引摘要（稿件版本未注明）