An Empirical Study of Stabilities of Estimators and Variance Estimators in Unequal Probability Sampling (n = 3 or 4)
Bayless, D. L., & Rao, J. N. K. (1970). An Empirical Study of Stabilities of Estimators and Variance Estimators in Unequal Probability Sampling (n = 3 or 4). Journal of the American Statistical Association, 65(332), 1645-1667.
Rao and Bayless  empirically investigated the stabilities of estimators of the population total and stabilities of their variance estimators for several methods of unequal probability sampling of two units $(n = 2)$ per stratum. In this article, after deriving the variances of variance estimators for general $n$ for the following methods: (a) the I.P.P.S. (inclusion probabilities proportional to size) methods of Fellegi, Sampford and Carroll-Hartley, (b) Des Raj's and Murthy's methods, (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, we perform empirical studies for $n = 3$ and 4 along the lines of our previous article. A major conclusion is that Murthy's method may be preferable over the other methods when a stable estimator as well as a stable variance estimator are required