On the relative efficiency of Murthy's sampling strategy under a super population model

Article type: Research Article

Authors: Sengupta, S.

Affiliations: Department of Statistics, University of Calcutta, 35, Ballygunge Circular Road, Kolkata 700019, India. E-mail: [email protected]

Abstract: Rao (1966), Hanurav (1967), Rao (1967) and Chaudhuri and Arnab (1979) had compared the model expected variances of the Horvitz - Thompson (1952) estimator (eHT) based on inclusion probability proportional to size (IPPS) sampling design, the Rao - Hartley - Cochran (1962) estimator (eRHC) and the ratio estimator (eMS) based on Midzuno - Sen (1952, 1953) sampling scheme for estimating a finite population total under a super-population model M involving a parameter g and had shown that the model expected variance is least for eHT if g > 1 and for eMS if g < 1 while for g = 1, the relative efficiencies are equal for all the three estimators. In this note we compare the relative efficiencies of eHT and the Murthy's (1957) estimator (eM) based on probability proportional to size without replacement (PPSWOR) sampling scheme under M and prove that the model expected variance is smaller for eM if g ≤ 1 and for eHT if g ≥ 2. In particular, it follows that for g = 1, eM is more efficient than each of eHT, eRHC and eMS which had been proved in Rao (1966) only for samples of size two.

Keywords: Finite population total, relative efficiency, super-population model, unbiased sampling strategies

DOI: 10.3233/MAS-160365

Journal: Model Assisted Statistics and Applications, vol. 11, no. 3, pp. 231-234, 2016