Consistency of estimators and variance estimators for two-stage sampling
share
Two-stage sampling designs are commonly used for household and health surveys. To produce reliable estimators with assorted confidence intervals, some basic statistical properties like consistency and asymptotic normality of the Horvitz-Thompson estimator are desirable , along with the consistency of assorted variance estimators. These properties have been mainly studied for single-stage sampling designs. In this work, we prove the consistency of the Horvitz-Thompson es-timator and of associated variance estimators for a general class of two-stage sampling designs, under mild assumptions. We also study two-stage sampling with a large entropy sampling design at the first stage, and prove that the Horvitz-Thompson estimator is asymptot-ically normally distributed through a coupling argument. When the 1 first-stage sampling fraction is negligible, simplified variance estima-tors which do not require estimating the variance within the Primary Sampling Units are proposed, and shown to be consistent.
READ FULL TEXT