Statistical Methods and Applications

, Volume 16, Issue 3, pp 309–319 | Cite as

Multi-phase sampling under cost constraints

  • Giancarlo Diana
  • Chiara Tommasi
  • Paolo PreoEmail author
Original Article


Multi-phase sampling (M-PhS) scheme is useful when the interest is in the estimation of the population mean of an expensive variable strictly connected with other cheaper (auxiliary) variables. The MSE is an accuracy measure of an estimator. Usually it decreases as the sample size increases. In practice the sample size cannot become arbitrarily large for possible cost constraints. From a practical point of view it would be useful to know the sample sizes which guarantee the best accuracy of the estimates for fixed costs. These “optimum” sample sizes can be, in some cases, computable but not admissible. In other cases, they can be neither admissible nor computable. The main goal of this paper is to propose a solution for both these situations. It will be clear that in both situations the solution is to consider a M-PhS scheme with one or more phases less.


Auxiliary variables Cost constraints Multi-phase sampling Optimality 


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  1. Ahmed MS (2003) General chain estimators under multi phase sampling. J Appl Stat Sci 12(4):243–250zbMATHGoogle Scholar
  2. Cochran WG (1977) Sampling techniques, 3rd edn. Wiley, New YorkzbMATHGoogle Scholar
  3. Diana G, Tommasi C (2003) Optimal estimation for finite population mean in two-phase sampling. Stat Meth Appl 12:41–48zbMATHCrossRefMathSciNetGoogle Scholar
  4. Diana G, Tommasi C, Preo P (2004) Estimation for finite population mean under multi-phase sampling. Atti della XLII Riunione Scientifica SIS, Bari pp 525–528Google Scholar
  5. Mukerjee R, Rao TJ, Vijayan K (1987) Regression type estimators using multiple auxiliary information. Austral J Stat 29(3):244–254MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Dipartimento di Scienze StatisticheUniversità degli Studi di PadovaPadovaItaly
  2. 2.Dipartimento di Economia Politica ed AziendaleUniversità degli Studi di MilanoMilanoItaly

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