Statistical Papers

, Volume 39, Issue 3, pp 313–319 | Cite as

Conditional MSE-based discrimination of the sample mean and the post-stratification estimator in population sampling

  • Gregor Dorfleitner


Whenever a random sample is drawn from a stratified population, the post-stratification estimator\(\tilde X\) usually is preferred to the sample mean\(\tilde X\), when the population mean is to be estimated. This is due to the fact that the variance of\(\tilde X\) is asymptotically smaller than that of\(\tilde X\), while both estimators are asymptotically unbiased. However, this only holds looking at post-stratification unconditionally, when strata sample sizes are random. Conditioned on the realized sample sizes, the MSE of\(\tilde X\) can be higher than that of\(\tilde X\) which means that\(\tilde X\) should be preferred to\(\tilde X\), even if it is biased. The conditional MSE difference of\(\tilde X\) and\(\tilde X\) is estimated, and using this estimation and its variance a heuristic test based on the Vysochanskiî-Petunin inequality is derived.


Post-stratification conditional inference Vysochanskiî-Petunin inequality superpopulation model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Cochran, W.G. (1963):Sampling Techniques, Second Edition. Wiley, New York.Google Scholar
  2. Hogg, R.V. (1974): Adaptive Robust Procedures: A Partial Review and Some Suggestions for Future Applications and Theory,Journal of the American Statistician Association 69: 909–923CrossRefMathSciNetzbMATHGoogle Scholar
  3. Holt, D.; Smith, T.M.F. (1979): Post Stratification.Journal of the Royal Statistical Society A 142: 33–46CrossRefGoogle Scholar
  4. Pokropp, F. (1996):Stichproben: Theorie und Verfahren. Oldenbourg, München.Google Scholar
  5. Sclove, S.L.; Morris C., Radhakrishnan, R. (1972): Non-Optimality of Preliminary-Test Estimators for the Mean of a Multivariate Normal-Distribution,The Annals of Mathematical Statistics 43: 1481–1490CrossRefMathSciNetzbMATHGoogle Scholar
  6. Sellke, T. (1996): Generalized Gauss-Chebyshev Inequalities for Unimodal Distributions.Metrika 43: 107–121CrossRefMathSciNetzbMATHGoogle Scholar
  7. Särndal, C.-E.; Swensson, B.; Wretman, J. (1992):Model Assisted Survey Sampling. Springer, New York.zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Gregor Dorfleitner
    • 1
  1. 1.Institut für Statistik und Mathematische WirtschaftstheorieUniversität AugsburgAugsburgGermany

Personalised recommendations