An Empirical Study of the Stabilities of Estimators and Variance Estimators in Unequal Probability Sampling of Two Units per Stratum

Abstract

Stabilities of estimators of the population total and stabilities of their variance estimators are compared for the following methods of sampling two units per stratum: (a) the I.P.P.S. (inclusion probabilities proportional to size) methods of Brewer, Fellegi and Hanurav using the Horvitz-Thompson estimator, (b) Des Raj's and Murthy's methods of p.p.s. sampling without replacement, (c) the Rao-Hartley-Cochran method, (d) Lahiri's method using a ratio estimator and (e) p.p.s. sampling with replacement using the customary estimator. A wide variety of populations, natural as well as artificial, is used for this purpose. The empirical study is supplemented by a semitheoretical study based on an often-used super-population model. The two studies lead to the following major conclusions: (1) Murthy's method is preferable over the other methods when a stable estimator as well as a stable variance estimator are required. (2) The Rao-Hartley-Cochran variance estimator is the most stable, but their estimator might lead to significant losses in efficiency. (3) Hanurav's method does not lead to significant improvements over Fellegi's or Brewer's methods with regard to stability of the variance estimator.