Skip to main content

Entropic Shifting Perspectives and Applications

  • Chapter
  • First Online:
The Information Theory of Comparisons
  • 662 Accesses

Abstract

With the passage of time or circumstance, probability distributions change; and as they do so, the allocation of entropic complexity likewise changes. The present chapter develops a systematic way of modelling such developments, with partition entropy as the organising framework. This leads to unit left and right entropic shifts, enabling a calculus of partial left and right shifts, concentrators and spreaders. Applications include data smoothing and end correction, social dynamics of opinions, and financial risk management.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 99.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Asch, S. E. (1955). Opinions and social pressure. Scientific American, 193, 31–35.

    Article  Google Scholar 

  • Bikhchandani, S., Hirshleifer, D., & Welch, I. (1992). A theory of fads, fashion, custom, and cultural change as informational cascades. Journal of Political Economy, 100, 992–1026.

    Article  Google Scholar 

  • Billingsley, P. (1986) Probability and measure (3rd ed.). Hoboken N.Y.: Wiley.

    Google Scholar 

  • Blaesche, T., Bowden R. J., & Posch, P. N. (2014). Data smoothing and end correction using entropic kernel compression. Stat: International Statistics Association, 3, 250–257.

    Article  Google Scholar 

  • Boneva, L. I., Kendall, D. G., & Stefanov, I. (1971). Spline transformations: Three new diagnostic aids for the statistical data analyst. Journal of the Royal Statistical Society Series B, 33, 1–70.

    MathSciNet  MATH  Google Scholar 

  • Bowden, R. J. (1987). Repeated sampling in the presence of publication effects. Journal of the American Statistical Association, 82, with commentaries by P.C. Ordeshook and L.S. Cahoon, 476-484/91.

    Article  MathSciNet  Google Scholar 

  • Bowden, R. J. (1988). Statistical games and human affairs. New York: Cambridge University Press; electronic ed. 2009.

    Google Scholar 

  • Bowden, R. J. (2012). Information, measure shifts and distribution metrics. Statistics, A Journal of Theoretical and Applied Statistics, 46, 249–262.

    MathSciNet  MATH  Google Scholar 

  • Bowden, R. J. (2013). Entropic kernels for data smoothing. Statistics & Probability Letters, 83, 916–922.

    Article  MathSciNet  Google Scholar 

  • Brewer, P. R. (2014a). Public opinion about gay rights and gay marriage. International Journal of Public Opinion Research, 26, 279–282.

    Article  Google Scholar 

  • Brewer, P. R. (ed.) (2014b). Special issue: Public opinion on gay rights and marriage. International Journal of Public Opinion Research, 26(3), 283–300.

    Google Scholar 

  • Di Crescenzo, A., & Toomaj, A. (2015). Extension of the past lifetime and its connection to the cumulative residual entropy. Journal of Applied Probability, 52, 1156–1174.

    Article  MathSciNet  Google Scholar 

  • Epanechnikov, V. A. (1969). Nonparametric estimation of a multivariate probability density. Theory of Probability and Applications, 14, 153–158.

    Article  MathSciNet  Google Scholar 

  • Gasser, T., & Muller, H. G. (1984). Estimating regression functions and their derivatives by the kernel method. Scandinavian Journal of Statistics, 11, 171–185.

    MathSciNet  MATH  Google Scholar 

  • Ghosh, B. K., & Huang, W.-M. (1992). Optimum bandwidths and kernels for estimating certain discontinuous densities. Annals of the Institute of Statistical Mathematics, 44, 563–577.

    MathSciNet  MATH  Google Scholar 

  • Jones, M. C. (1993). Simple boundary correction for kernel density estimations. Statistics & Computing, 3, 135–146.

    Article  Google Scholar 

  • Jorion, P. (2003). Financial risk manager handbook (2nd ed.). New York: Wiley.

    Google Scholar 

  • Kapodistria, S., & Psarrakos, G. (2012). Some extensions of the residual lifetime and its connection to the cumualtive residual entropy. Probability in the Engineering and Informational Sciences, 26, 129–146.

    Article  MathSciNet  Google Scholar 

  • Nadaraya, E. A. (1964). On estimating regression. Theory of Probability and Applications, 9, 141–142.

    Article  Google Scholar 

  • Priestley, M. B., & Chao, M. T. (1972). Non-parametric function fitting. Journal of the Royal Statistical Society, B34, 385–392.

    MathSciNet  MATH  Google Scholar 

  • Rao, M., Chen, Y., Vemuri, B. C., & Wang, F. (2004). Cumulative residual entropy: A new measure of information. IEEE Transaction Information Theory, 50, 1220–1228.

    Article  MathSciNet  Google Scholar 

  • Rice, J. A. (1984). Boundary modification for kernel regression. Communications in Statistics: Theory & Methods, 13, 893–900.

    Article  MathSciNet  Google Scholar 

  • Saunders, A., & Cornett, M. M. (2006). Financial institutions management: A risk management perspective (5th ed.). New York: McGraw-Hill.

    Google Scholar 

  • Schuster, E. F. (1985). Incorporating support constraints into nonparametric estimators of densities. Communications in Statistics: Theory & Methods, 14, 1123–1136.

    Article  MathSciNet  Google Scholar 

  • Shilov, G. E., & Gurevich, B. L. (1977). Integral, measure and derivative: A unified approach. New York: Dover.

    Google Scholar 

  • Silverman, B. W. (1986). Density estimation for statistics and data analysis. London: Chapman & Hall.

    Book  Google Scholar 

  • Tahmasebi, S., Eskandarzadeh, M., & Ali Akbar, J. (2017). An extension of generalized cumulative residual entropy. Journal of Statistical Theory and Applications, 16, 165–177.

    Article  MathSciNet  Google Scholar 

  • Wand, M. P., & Jones, M. C. (1995). Kernel smoothing. Monographs on Statistics and Applied Probability. London: Chapman and Hall.

    Google Scholar 

  • Watson, G. C. (1964) Smooth regression analysis. Sankhya A. 359–372.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Roger Bowden .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bowden, R. (2018). Entropic Shifting Perspectives and Applications. In: The Information Theory of Comparisons. Springer, Singapore. https://doi.org/10.1007/978-981-13-1550-3_2

Download citation

Publish with us

Policies and ethics