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Zümre sınırlarının seçilmesi: Bulunması zor optimumlar

Year 2010, Volume: 39 Issue: 2, 195 - 204, 02.12.2009

Abstract

Dalenius’un (1950) zümre sınırlarının belirlenmesi için bir denklem kümesi sağlamasının ardından, ortalamanın ya da toplamın Horvitz-Thompson tahminleyeninin varyansını minimize eden optimum zümre sınırlarını elde etmek için yapılan çalışmalar giderek yaygınlaşmıştır. Bu makalede, gerçekleştirilen yöntemlerin gelişimi takip edilerek şu anda hangi aşamada olduğumuz ve bulunduğumuz noktadan nereye gidebileceğimiz sorularına cevap aranmaktadır. 

References

  • W.G. Cochran, Sampling Techniques, New York: Wiley, 1977.
  • T. Dalenius, and J.L. Hodges, Minimum Variance Stratification. Journal of the American Statistical Association. 88-101 (1959).
  • W.G. Cochran, Comparison of Methods for Determining Stratum Boundaries. Bulletin of the International Statistical Institute. 32, 2, 345-358 (1961).
  • D. Hedlin, A Procedure of Stratification by an Extended Ekman Rule. Journal of Official Statistics. 16, 15-29 (2000).
  • P. Lavallée, and M. Hidiroglou, On the Stratification of Skewed Populations. Survey Methodology. 14, 33-43 (1988).
  • V.K. Sethi, A Note on the Optimum Stratification of Populations for Estimating the Population Means. Australian Journal of Statistics. 5, 20-33 (1963).
  • R. Detlefsen, and L. Veum, Design issues for the Retail Trade Survey in the U.S. Bureau of the Census. Proceedings of the Research Method Section. American Accounting Association, 214-219 (1991).
  • J. Slanta, and T. Krenzke, Applying Lavallée and Hidiroglou Method to obtain Stratification Boundaries for the Census Bureau's Annual Capital Expenditure Survey. Survey Methodology. 22, 65-75 (1996).
  • M. Kozak, Optimal Stratification Using Random Search Method in Agricultural Surveys. Statistics in Transition. 6, 5, 797-806 (2004).
  • J. Neyman, On the Two Different Aspects of the Representative Method: The Method of Stratified Sampling and the Method of Purposive Selection. Journal of the Royal Statistics Society. 97, 558—606 (1934).
  • S. Baillargeon, and L.P. Rivest, Univariate Stratification of Survey Populations, R Package, available on the CRAN website at http://www.r-project.org/. 2010.
  • S. Baillargeon, and L.P. Rivest, A General Algorithm or Univariate Stratification. International Statistical Review. 77, 3, 331-344 (2009).
  • T. Keskinturk, and S. Er, A Genetic Algorithm Approach to Determine Stratum Boundaries and Sample Sizes of Each Stratum in Stratified Sampling. Computational Statistics and Data Analysis. 52, 1, 58-67 (2007).
  • M.G.M. Khan, N. Nand, and N. Ahmad, Determining the Optimum Stratum Boundary Points Using Dynamic Programming. Survey Methodology. 34, 205-214 (2008).
  • J. Brito, et al., An ILS Approach applied to Optimum Stratification Problem, 2009.
  • J. Brito, et al., An Exact Algorithm for the Stratification with Proportional Allocation. Optim Lett. 4, 185-195 (2010)
  • P. Gunning, and J.M. Horgan, A New Algorithm for the Construction of Stratum Boundaries in Skewed Populations. Survey Methodology. 2, 30, 159-166 (2004).
  • J.M. Horgan, Stratification of Skewed Populations: A Review. The International Statistics Review. 74, 67-76 (2006).
  • J.M. Horgan, A List Sequential Sampling Scheme with Applications in Financial Auditing. IMA Journal of Management Mathematics. 14, 1-18 (2003).
  • M. Evans, N.A.J. Hastings, and J.B. Peacock, Statistical Distributions. 3rd Edition, New York: Wiley, 2000.
  • P. Gunning, J.M Horgan, and G. Keogh, Efficient Pareto Stratification. Mathematical Proceedings of the Royal Irish Academy. 106, 2, 131-138 (2006).
  • P. Gunning, and J.M. Horgan, Improving the \LH Algorithm for Stratification of Skewed Populations. Journal of Statistical Computation and Simulation. 4, 77, 277291 (2007).
  • P.Gunning, J.M, Horgan, and G. Keogh, An Implementation Strategy for Efficient Convergence of \LH Stratification. Journal of Official Statistics. 213-228 (2008).
  • M. Kozak, and M. Verma, Geometric versus Optimization to Stratification: A Comparison of Efficiency. Survey Methodology. 32, 2, 157-183 (2006).
  • C. Sarndal, B. Swensson, and J. Wretman, Model Assisted Survey Sampling. Springer, 1992.

Choosing the stratification boundaries: The elusive optima

Year 2010, Volume: 39 Issue: 2, 195 - 204, 02.12.2009

Abstract

Since Dalenius (1950) provided a set of equations for the determination of the stratum boundaries, there has been a proliferation of attempts to obtain the optimum stratum boundaries, those that minimise the variance of the Horvitz-Thompson estimator of mean or total. In this paper, we track the progress of such methods, and ask where we are now and where to go from here. 

References

  • W.G. Cochran, Sampling Techniques, New York: Wiley, 1977.
  • T. Dalenius, and J.L. Hodges, Minimum Variance Stratification. Journal of the American Statistical Association. 88-101 (1959).
  • W.G. Cochran, Comparison of Methods for Determining Stratum Boundaries. Bulletin of the International Statistical Institute. 32, 2, 345-358 (1961).
  • D. Hedlin, A Procedure of Stratification by an Extended Ekman Rule. Journal of Official Statistics. 16, 15-29 (2000).
  • P. Lavallée, and M. Hidiroglou, On the Stratification of Skewed Populations. Survey Methodology. 14, 33-43 (1988).
  • V.K. Sethi, A Note on the Optimum Stratification of Populations for Estimating the Population Means. Australian Journal of Statistics. 5, 20-33 (1963).
  • R. Detlefsen, and L. Veum, Design issues for the Retail Trade Survey in the U.S. Bureau of the Census. Proceedings of the Research Method Section. American Accounting Association, 214-219 (1991).
  • J. Slanta, and T. Krenzke, Applying Lavallée and Hidiroglou Method to obtain Stratification Boundaries for the Census Bureau's Annual Capital Expenditure Survey. Survey Methodology. 22, 65-75 (1996).
  • M. Kozak, Optimal Stratification Using Random Search Method in Agricultural Surveys. Statistics in Transition. 6, 5, 797-806 (2004).
  • J. Neyman, On the Two Different Aspects of the Representative Method: The Method of Stratified Sampling and the Method of Purposive Selection. Journal of the Royal Statistics Society. 97, 558—606 (1934).
  • S. Baillargeon, and L.P. Rivest, Univariate Stratification of Survey Populations, R Package, available on the CRAN website at http://www.r-project.org/. 2010.
  • S. Baillargeon, and L.P. Rivest, A General Algorithm or Univariate Stratification. International Statistical Review. 77, 3, 331-344 (2009).
  • T. Keskinturk, and S. Er, A Genetic Algorithm Approach to Determine Stratum Boundaries and Sample Sizes of Each Stratum in Stratified Sampling. Computational Statistics and Data Analysis. 52, 1, 58-67 (2007).
  • M.G.M. Khan, N. Nand, and N. Ahmad, Determining the Optimum Stratum Boundary Points Using Dynamic Programming. Survey Methodology. 34, 205-214 (2008).
  • J. Brito, et al., An ILS Approach applied to Optimum Stratification Problem, 2009.
  • J. Brito, et al., An Exact Algorithm for the Stratification with Proportional Allocation. Optim Lett. 4, 185-195 (2010)
  • P. Gunning, and J.M. Horgan, A New Algorithm for the Construction of Stratum Boundaries in Skewed Populations. Survey Methodology. 2, 30, 159-166 (2004).
  • J.M. Horgan, Stratification of Skewed Populations: A Review. The International Statistics Review. 74, 67-76 (2006).
  • J.M. Horgan, A List Sequential Sampling Scheme with Applications in Financial Auditing. IMA Journal of Management Mathematics. 14, 1-18 (2003).
  • M. Evans, N.A.J. Hastings, and J.B. Peacock, Statistical Distributions. 3rd Edition, New York: Wiley, 2000.
  • P. Gunning, J.M Horgan, and G. Keogh, Efficient Pareto Stratification. Mathematical Proceedings of the Royal Irish Academy. 106, 2, 131-138 (2006).
  • P. Gunning, and J.M. Horgan, Improving the \LH Algorithm for Stratification of Skewed Populations. Journal of Statistical Computation and Simulation. 4, 77, 277291 (2007).
  • P.Gunning, J.M, Horgan, and G. Keogh, An Implementation Strategy for Efficient Convergence of \LH Stratification. Journal of Official Statistics. 213-228 (2008).
  • M. Kozak, and M. Verma, Geometric versus Optimization to Stratification: A Comparison of Efficiency. Survey Methodology. 32, 2, 157-183 (2006).
  • C. Sarndal, B. Swensson, and J. Wretman, Model Assisted Survey Sampling. Springer, 1992.
There are 25 citations in total.

Details

Primary Language English
Journal Section Statistics
Authors

Jane Horgan This is me

Publication Date December 2, 2009
Published in Issue Year 2010 Volume: 39 Issue: 2

Cite

APA Horgan, J. (2009). Choosing the stratification boundaries: The elusive optima. İstanbul Üniversitesi İşletme Fakültesi Dergisi, 39(2), 195-204.
AMA Horgan J. Choosing the stratification boundaries: The elusive optima. İstanbul Üniversitesi İşletme Fakültesi Dergisi. December 2009;39(2):195-204.
Chicago Horgan, Jane. “Choosing the Stratification Boundaries: The Elusive Optima”. İstanbul Üniversitesi İşletme Fakültesi Dergisi 39, no. 2 (December 2009): 195-204.
EndNote Horgan J (December 1, 2009) Choosing the stratification boundaries: The elusive optima. İstanbul Üniversitesi İşletme Fakültesi Dergisi 39 2 195–204.
IEEE J. Horgan, “Choosing the stratification boundaries: The elusive optima”, İstanbul Üniversitesi İşletme Fakültesi Dergisi, vol. 39, no. 2, pp. 195–204, 2009.
ISNAD Horgan, Jane. “Choosing the Stratification Boundaries: The Elusive Optima”. İstanbul Üniversitesi İşletme Fakültesi Dergisi 39/2 (December 2009), 195-204.
JAMA Horgan J. Choosing the stratification boundaries: The elusive optima. İstanbul Üniversitesi İşletme Fakültesi Dergisi. 2009;39:195–204.
MLA Horgan, Jane. “Choosing the Stratification Boundaries: The Elusive Optima”. İstanbul Üniversitesi İşletme Fakültesi Dergisi, vol. 39, no. 2, 2009, pp. 195-04.
Vancouver Horgan J. Choosing the stratification boundaries: The elusive optima. İstanbul Üniversitesi İşletme Fakültesi Dergisi. 2009;39(2):195-204.