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Introduction to Estimation Methods

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Probability, Statistical Optics, and Data Testing

Part of the book series: Springer Series in Information Sciences ((SSINF,volume 10))

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  • The book was inadvertently published with missing figures in several chapters of this book. This has been added in the affected chapters.

Abstract

The general aim of statistics is to infer something about the source that gave rise to given data. An ultimate aim is to find exact numerical values for the source. There is a large body of literature on this subject, called estimation theory. Estimation is both an art and a science — typical of most subjects in statistics. Hence, there are passionate devotees of one approach or another, to a given problem, especially economic problems. Personally, we like the following motivation for the subject: If Adam and Eve were expelled from Paradise for attempting to Know, then the least we can do, having lost our chance at earthly Paradise, is to find out just how well we can Know.

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References

  1. B.R. Frieden: Phys. Rev. A41, 4265 (1990)

    Article  ADS  Google Scholar 

  2. H.L. Van Trees: Detection, Estimation and Modulation Theory, Part I (Wiley, New York 1968)

    MATH  Google Scholar 

  3. B.R. Frieden: Appl. Opt. 26, 1755 (1987)

    Article  ADS  Google Scholar 

  4. R. Kikuchi, B.H. Soffer: J. Opt. Soc. Am. 67, 1656 (1977)

    Article  ADS  Google Scholar 

  5. B.R. Frieden: Am. J. Phys. 57, 1004 (1989)

    Article  ADS  Google Scholar 

  6. B.R. Frieden: Opt. Lett. 14, 199 (1989)

    Article  ADS  Google Scholar 

  7. T.D. Milster et al.: J. Nucl. Med. 31, 632 (1990)

    Google Scholar 

  8. A.J. Stam: Inform, and Control 2, 101 (1959)

    Article  Google Scholar 

  9. A. Bhattacharyya: Sankhya 8, 1, 201, 315 (1946-1948)

    MathSciNet  Google Scholar 

  10. B.R. Martin and G. Shaw: Particle Physics (Wiley, New York 1992)

    MATH  Google Scholar 

  11. B.R. Frieden and A. Plastino: Phys. Letts. A 278, 299 (2001)

    Article  ADS  Google Scholar 

  12. B.R. Frieden: Physics from Fisher Information: a Unification (Cambridge Univ. Press, England 1998)

    Book  MATH  Google Scholar 

  13. I. Kant: Kritik der reinen Vernunft (J.F. Hartknoch, Riga 1787). Also, English transl., Critique of Pure Reason (Willey Book Co., New York 1900)

    Google Scholar 

  14. J.D. Jackson: Classical Electrodynamics, 2nd. ed. (Wiley, New York 1975)

    MATH  Google Scholar 

  15. M.B. Mensky: Phys. Rev. D 20, 384 (1979); also, Continuous Quantum Measurements and Path Integrals (Inst. of Physics Publ., Bristol, England 1993)

    Article  ADS  Google Scholar 

  16. J.A. Wheeler: in Proceedings of the 3rd International Symposium on Foundations of Quantum Mechanics, Tokyo, 1989, eds. S. Kobayashi et. al. (Physical Society of Japan, Tokyo 1990), 354; also: in Physical Origins of Time Asymmetry, eds. J.J. Halliwell et. al. (Cambridge Univ. Press, England 1994), 1–29

    Google Scholar 

  17. B.R. Frieden and B.H. Soffer: Phys. Rev. E 52, 2274 (1995)

    Article  ADS  Google Scholar 

  18. B.R. Frieden and A. Plastino: Physics Letts. A 272, 326 (2000)

    Article  ADS  Google Scholar 

  19. L. Brillouin: Science and Information Theory: (Academic, New York 1956)

    Book  MATH  Google Scholar 

  20. H. Goldstein: Classical Mechanics (Addison-Wesley, Cambridge Mass 1956), p. 365

    Google Scholar 

  21. P.M. Morse and H. Feshbach: Methods of Theoretical Physics, Part I (McGraw-Hill, New York 1953), p. 278

    MATH  Google Scholar 

  22. G.V. Vstovsky: Phys. Rev. E 51, 975 (1995)

    Article  ADS  Google Scholar 

  23. H. Risken: The Fokker-Planck Equation (Springer-Verlag, Berlin 1984)

    Book  MATH  Google Scholar 

  24. A.R. Plastino and A. Plastino: Phys. Rev. E 54, 4423 (1996)

    Article  ADS  Google Scholar 

  25. C. Villani and G. Toscani: Comm. Math. Phys. 203, 667 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  26. P.M. Binder: Phys. Rev. E 61, R3303 (2000)

    Article  ADS  Google Scholar 

  27. R. Badii and A. Politi: Complexity: Hierarchical Structure and Scaling in Physics (Cambridge Univ. Press, England 1997)

    Book  MATH  Google Scholar 

  28. W.J. Cocke: Phys. of Fluids 8, 1609 (1996)

    Article  ADS  Google Scholar 

  29. E. Giulini et. al.: Decoherence and the Appearance of a Classical World in Quantum Theory (Springer-Verlag, Berlin 1996)

    Book  MATH  Google Scholar 

  30. H.D. Zeh: “What is achieved by decoherence?”, in: New Developments on Fundamental Problems in Quantum Physics, eds. M. Ferrero and A. van der Merwe (Kluwer Academic, Dordrecht, Netherlands 1997)

    Google Scholar 

  31. R.A. Tapia and J.R. Thompson: Nonparametric probability density estimation (Johns Hopkins Univ. Press, Baltimore 1978)

    MATH  Google Scholar 

  32. B.R. Frieden, Am. J. Physics 57, 1004 (1989); also Phys. Rev. A 41, 4265 (1990)

    Article  ADS  Google Scholar 

  33. P.H. Cootner, ed: The Random Character of Stock Market Prices (MIT Press, Cambridge, Massachusetts 1964)

    Google Scholar 

  34. R.J. Hawkins, M. Rubinstein and G.J. Daniell: “Reconstruction of the probability density function implicit in option prices from incomplete and noisy data,” in: Proceedings of the Fifteenth International Workshop on Maximum Entropy and Bayesian Methods, eds. K.M. Hanson and R.N. Silver (Kluwer Academic, Dordrecht, Netherlands 1996)

    Chapter  MATH  Google Scholar 

  35. G.A. Korn and T.M. Korn: Mathematical Handbook for Scientists and Engineers, 2nd. ed. (McGraw-Hill, New York 1968)

    MATH  Google Scholar 

  36. B.R. Frieden, A. Plastino, A.R. Plastino and B.H. Soffer, Phys. Rev. E 60, 48 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  37. J.A. Eisele: Modern quantum mechanics with applications to elementary particle physics (Wiley, New York 1969), 37

    MATH  Google Scholar 

Additional Reading

  • J-P. Bouchard and M. Potters: Theory of Financial Risk: From Statistical Physics to Risk Management (Cambridge Univ. Press, England 2000)

    Google Scholar 

  • T. Cover and J. Thomas: Elements of Information Theory (Wiley, New York 1991)

    Book  MATH  Google Scholar 

  • I.J. Good: in Foundations of Probability Theory, Statistical Inference and Statistical Theories of Science, Vol II, eds. W.L. Harper and C.A. Hooker (Reidel, Boston 1976)

    Google Scholar 

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Authors and Affiliations

  1. Optical Research Center, University of Arizona, Tucson, AZ, 85721, USA

    Professor B. Roy Frieden

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  1. Professor B. Roy Frieden
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© 2001 Springer-Verlag Berlin Heidelberg

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Frieden, B.R. (2001). Introduction to Estimation Methods. In: Probability, Statistical Optics, and Data Testing. Springer Series in Information Sciences, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56699-8_17

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  • DOI: https://doi.org/10.1007/978-3-642-56699-8_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41708-8

  • Online ISBN: 978-3-642-56699-8

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