3rd International Young Scientist Congress(IYSC-2017).  International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

Admissible Estimation of a Finite Population Total under PPS Sampling

Author Affiliations

  • 1Department of Statistics, Sardar Patel University, Vallabh Vidyanagar 388 120, India
  • 2St. Xevier’s College, Gujarat University, Ahmedabad-380 009, India

Res. J. Mathematical & Statistical Sci., Volume 4, Issue (10), Pages 10-15, November,12 (2016)


The probability proportion to size (PPS) and with replacement estimator is inadmissible since it depends on multiplicity. An improve estimator is available but it is too complicated. Using the Bayes prediction approach a Bayes predictor, based on the distinct units of the sample selected with PPS sampling, is constructed which includes a generalized difference estimator of the population total. Moreover, using the limiting Bayes risk method it is shown that this predictor is admissible. For comparison of the suggested estimator, a generalize regression estimator and an optimal estimator (with distinct units) are discussed. Using real populations, a small scale Monte Carlo simulation is carried out for the comparison of estimators. It is found that the suggested estimator has performed very well for most of the real populations under investigation.


  1. Hansen M.H. and W.N. Hurwitz (1943)., On the theory of sampling from finite populations., Ann. Math. Statist., 14, 333–362.
  2. Basu D. (1958)., On sampling with and without replacemen., Sankhya 20, 287-294.
  3. Subrahmanya M.T. (1966)., A note on a biased estimator in sampling with probability proportional to size with replacement., Ann. of Maths. and Statist., 37(4), 1045-1047.
  4. Pathak P.K. (1962)., On simple random sampling with replacement., Sanskya A: The Indian Journal of Statistics, 24, 287-302
  5. Godambe V.P. (1960)., An admissible estimate for any sampling design., Sankhyā: The Indian Journal of Statistics, 22, 285-288.
  6. Lehmann E.L. and Casella G. (1998)., Theory of Point Estimation., 2nd Edition, Springer.
  7. Särndal C.E., Swensson B. and Wretman J.H. (1992)., Model Assisted Survey Sampling., Springer Verlag, New York.
  8. Montanari G.E. (1998)., On regression estimation of finite population means., Survey Methodology, 24, 69-77.
  9. Train K. (2003)., Discrete Choice Methods with Simulation., Cambridge University Press.
  10. Bolfarine H. (1987)., Minimax prediction in finite populations., Comm. in Statist-Theory Meth., 16(12), 3683-3700.
  11. Raiffa H. and Schlaifer R.O. (1961)., Applied Statistical Decision Theory., Harvard University.
  12. Hedayat A.S. and Sinha B.K. (1991)., Design and Inference in finite population sampling., John Wiley, New York.
  13. Murthy M.N. (1967)., Sampling Theory and Methods., Statistical Publishing House: Culcutta.