Observing that the estimator for a “finite population variance” as recommended byLiu [1974a, b] can sometimes become negative, we suggest a few non-negative alternative estimators and note some of their properties. UnlikeLiu we follow the conventional Bayesian approach to get another estimator with an optimal property of “uniform admissibility”.
KeywordsStochastic Process Probability Theory Economic Theory Bayesian Approach Population Variance
Unable to display preview. Download preview PDF.
- Godambe, V.P.: Admissibility and Bayes estimation in sampling finite populations. V. Ann. Math. Statist.40, 1969, 672–676.Google Scholar
- Ha'jek, J.: Asymptotic theory of rejective sampling with varying probabilities from a finite population. Ann. Math. Statist.35, 1964, 1491–1523.Google Scholar
- Hanurav, T.V.: Some aspects of unified sampling theory. Sankhyā, Ser. A,28, 1966, 175–204.Google Scholar
- Liu, T.P.: Bayes estimation for the variance of a finite population. Metrika21, 1974a, 127–132.Google Scholar
- : A general unbiased estimator for the variance of a finite population. Sankhyā, Ser. C,36, Part 1, 1974b, 23–32.Google Scholar
- Mukhopadhyay, P.: A sampling scheme to realise a pre-assigned set of inclusion-probabilities of first two orders. Cal. Stat. Assoc. Bull.21, 1972, 87–122.Google Scholar