Variance estimation in sampling from finite populations

Abstract

Using data from several artificial and natural populations published in the sampling literature, an empirical study of the unequal probability without replacement sampling methods due to Brewer (1963a), Carroll and Hartley (1964), Des Raj (1956), Fellegi (1963), Hanurav (1967), Lahiri (1951), Murthy (1957), Rao-Hartley-Cochran (1962), and Sampford (1967) for sample sizes of two, three, and four is performed. The joint criterion of stability of the estimators and stability of the variance estimators is used to compare these methods. For these comparisons the variance of the variance estimators had to be derived. The approach to normality of the estimators was also studied using the skewness and kurtosis of the estimators. For this, the derivation of the third and fourth central moments of the estimators were derived. Computer computational schemes to calculate the joint inclusion probabilities for these methods are also developed. The empirical study is supplemented with a semi-theoretical study based on a super-population model. Finally, following the methods of Brewer (1963b) and more detailedly that of Hanurav (1968), we develop a method to test the validity of the super population model and estimate its parameters.