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Invariant Embedding Technique and Its Applications for Improvement or Optimization of Statistical Decisions

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Analytical and Stochastic Modeling Techniques and Applications (ASMTA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6148))

Abstract

In the present paper, for improvement or optimization of statistical decisions under parametric uncertainty, a new technique of invariant embedding of sample statistics in a performance index is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant decision rule, which has smaller risk than any of the well-known decision rules. To illustrate the proposed technique, application examples are given.

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References

  1. Conrad, S.A.: Sales Data and the Estimation of Demand. Oper. Res. Quart. 27, 123–127 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  2. Liyanage, L.H., Shanthikumar, J.G.: A Practical Inventory Policy Using Operational Statistics. Operations Research Letters 33, 341–348 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Scarf, H.: Bayes Solutions of Statistical Inventory Problem. Ann. Math. Statist. 30, 490–508 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  4. Chu, L.Y., Shanthikumar, J.G., Shen, Z.J.M.: Solving Operational Statistics via a Bayesian Analysis. Operations Research Letters 36, 110–116 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bookbinder, J.H., Lordahl, A.E.: Estimation of Inventory Reorder Level Using the Bootstrap Statistical Procedure. IIE Trans. 21, 302–312 (1989)

    Article  Google Scholar 

  6. Scarf, H.: A Min–Max Solution of an Inventory Problem. Studies in the Mathematical Theory of Inventory and Production, ch. 12. Stanford University Press, Stanford (1958)

    Google Scholar 

  7. Gallego, G., Moon, I.: The Distribution Free Newsvendor Problem: Review and Extensions. J. Oper. Res. Soc. 44, 825–834 (1993)

    MATH  Google Scholar 

  8. Nechval, N.A., Nechval, K.N., Vasermanis, E.K.: Effective State Estimation of Stochastic Systems. Kybernetes 32, 666–678 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Nechval, N.A., Vasermanis, E.K.: Improved Decisions in Statistics. SIA “Izglitibas soli”, Riga (2004)

    Google Scholar 

  10. Nechval, N.A., Nechval, K.N.: Constrained Optimization in Newsboy Problems under Uncertainty via Statistical Inference Equivalence Principle. In: Al-Begain, K., Bolch, G., Telek, M. (eds.) Proceedings of the 12th International Conference on Analytical and Stochastic Modelling Techniques and Applications (ASMTA 2005), pp. 166–171, RTU, Riga, Latvia (2005)

    Google Scholar 

  11. Nechval, N.A., Berzins, G., Purgailis, M., Nechval, K.N.: Improved Estimation of State of Stochastic Systems via Invariant Embedding Technique. WSEAS Transactions on Mathematics 7, 141–159 (2008)

    MathSciNet  Google Scholar 

  12. Nechval, N.A., Nechval, K.N., Berzins, G., Purgailis, M., Rozevskis, U.: Stochastic Fatigue Models for Efficient Planning Inspections in Service of Aircraft Structures. In: Al-Begain, K., Heindl, A., Telek, M. (eds.) ASMTA 2008. LNCS, vol. 5055, pp. 114–127. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  13. Nechval, N.A., Berzins, G., Purgailis, M., Nechval, K.N., Zolova, N.: Improved Adaptive Control of Stochastic Systems. Advances in Systems Science and Applications  9, 11–20 (2009)

    Google Scholar 

  14. Hahn, G.J., Nelson, W.: A Survey of Prediction Intervals and their Applications. J. Qual. Tech. 5, 178–188 (1973)

    Google Scholar 

  15. Barlow, R.E., Proshan, F.: Tolerance and Confidence Limits for Classes of Distributions Based on Failure Rate. Ann. Math. Stat. 37, 1593–1601 (1966)

    Article  Google Scholar 

  16. Epstein, B., Sobel, M.: Some Theorems Relevant to Life Testing from an Exponential Population. Ann. Math. Statist. 25, 373–381 (1954)

    Article  MATH  MathSciNet  Google Scholar 

  17. Kendall, M.G., Stuart, A.: The Advanced Theory of Statistics, 3rd edn., vol. 1. Griffin, London (1969)

    MATH  Google Scholar 

  18. Grubbs, F.E.: Approximate Fiducial Bounds on Reliability for the Two Parameter Negative Exponential Distribution. Technometrics 13, 873–876 (1971)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. EVF Research Institute, Statistics Department, Nicholas Nechval, Maris Purgailis, Gundars Berzins, Kaspars Cikste, Juris Krasts, University of Latvia, Raina Blvd 19, LV-1050, Riga, Latvia

    Nicholas Nechval, Maris Purgailis, Gundars Berzins, Kaspars Cikste & Juris Krasts

  2. Transport and Telecommunication Institute, Applied Mathematics Department, Lomonosov Street 1, LV-1019, Riga, Latvia

    Konstantin Nechval

Authors
  1. Nicholas Nechval
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  2. Maris Purgailis
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  3. Gundars Berzins
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  4. Kaspars Cikste
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  5. Juris Krasts
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  6. Konstantin Nechval
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Editor information

Editors and Affiliations

  1. Faculty of Advanced Technology, University of Glamorgan, CF37 1DL, Pontypridd, UK

    Khalid Al-Begain

  2. Department TELIN, Ghent University, Sint-Pietersnieuwstraat 41, 9000, Gent, Belgium

    Dieter Fiems

  3. Department of Computing,, Imperial College London, South Kensington Campus, SW7 2AZ, London, United Kingdom

    William J. Knottenbelt

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Nechval, N., Purgailis, M., Berzins, G., Cikste, K., Krasts, J., Nechval, K. (2010). Invariant Embedding Technique and Its Applications for Improvement or Optimization of Statistical Decisions. In: Al-Begain, K., Fiems, D., Knottenbelt, W.J. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2010. Lecture Notes in Computer Science, vol 6148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13568-2_22

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  • DOI: https://doi.org/10.1007/978-3-642-13568-2_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13567-5

  • Online ISBN: 978-3-642-13568-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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