5th International Young Scientist Congress (IYSC-2019).  International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

Semiparametric and nonparametric calibration estimators in cluster sampling by use of penalty functions

Author Affiliations

  • 1Department of Statistics and Actuarial Sciences, Technical University of Kenya, P.O. BOX 52428-00200 Nairobi, Kenya

Res. J. Mathematical & Statistical Sci., Volume 6, Issue (4), Pages 1-10, April,12 (2018)


The application of nonparametric model calibration estimators in multistage survey sampling has been studied by several authors with the cluster level auxiliary information assumed completely available for each cluster. The reasoning behind model calibration is that if the calibration constraints are satisfied by the auxiliary variable, then it is expected that the fitted values of the variable of interest should satisfy such constraints too. In this paper, we have considered a case of auxiliary information present at two levels. We derive estimators by treating the calibration problems at both levels as optimization problems and solving them by the method of penalty functions. We have shown that the estimators obtained are robust since they do not fail in the event the model is misspecified for the data.


  1. Breidt F.J., Opsomer J.D., Johnson A.A. and Ranalli M.G. (2007)., Semiparametric model-assisted estimation for natural resource surveys., Survey Methodology, 33(1), 35.
  2. Kihara P.N., Otieno R.O. and Kihoro J.M. (2015)., Two Levels Model Calibration in Cluster Sampling; Use of Penalized Splines in Semiparametric Estimation., Mathematical Theory and Modeling, 5(4), 94-104.
  3. Kihara P.N. (2017)., Calibration Estimators by Penalty Function Method., Mathematical Theory and Modeling, 7(6), 22-32.
  4. Kihara P.N. (2017)., Robust Nonparametric and Semiparametric Model Calibration Estimators by Penalty Function Method., Mathematical Theory and Modeling, 7(8), 22-39.
  5. Deville J.C. and Sarndal C.E. (1992)., Calibration Estimators in Survey Sampling., Journal of the American Statistical Association, 87(418), 376-382.
  6. Wu C. and Sitter R.R. (2001)., A Model Calibration Approach to Using Complete Auxiliary Information from Survey Data., Journal of American Statistical Association, 96(453), 185-193.
  7. Rao S.S. (1984)., Optimization Theory and Applications., Wiley Eastern Limited, 390-424, ISBN: 0-85226-756-8.
  8. Simonof J. (1996)., Smoothing Methods in Statistics., New York: Springer, 40-93, ISBN: 0-387-94716-7
  9. Breidt F.J. and Opsomer J.D. (2000)., Local Polynomial Regression Estimation in Survey Sampling., Annals of Statistics, 28(4), 1026-1053.
  10. Montanari G.E. and Ranalli M.G. (2003)., Nonparametric Model Calibration Estimation in Survey Sampling., Journal of American Statistical Association, 100(472), 1429-1442.
  11. Kihara P.N. (2012)., Estimation of Finite Population Total in the Face of Missing Values Using Model Calibration and Model Assistance on Semiparametric and Nonparametric Models (Unpublished doctoral thesis)., Jomo Kenyatta University of Agriculture and Technology, Kenya.