Skip to main content

Hypothesis Testing for Squared Radial Ornstein–Uhleneck Model: Moderate Deviations Method

  • Conference paper
  • First Online:
  • 1091 Accesses

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 212))

Abstract

We study the moderate deviations for the log-likelihood ratio of the squared radial Ornstein-Uhleneck (O–U) model, with the help of them we give negative regions in testing squared radial O–U model, and get the decay rates of the error probabilities.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   329.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

References

  1. Neyman J, Pearson ES (1933) On the problem of the most efficient tests of statistical hypotheses. Phil Trans Roy Soc London 231:289–337

    Article  MATH  Google Scholar 

  2. Blahut RE (1984) Hypothesis testing and information theory. IEEE Trans Inform Theory 20:405–415

    Article  MathSciNet  MATH  Google Scholar 

  3. Chiyonobu T (2003) Hypothesis testing for signal detection problem and large deviations. Nagoya Math J 162:187–203

    Article  MathSciNet  MATH  Google Scholar 

  4. Gao FQ, Zhao SJ (2012) Moderate deviations and hypothesis testing for signal detection problem. Sci China Math 55:2273–2284

    Article  MathSciNet  MATH  Google Scholar 

  5. Han TS, Kobayashi K (1989) The strong converse theorem in hypothesis testing. IEEE Trans Inform Theory 35:178–180

    Article  MathSciNet  MATH  Google Scholar 

  6. Jiang H, Zhao SJ (2011) Large and moderate deviations in testing time inhomogeneous diffusions. J Stat Plan Infer 141:3160–3169

    Article  MathSciNet  MATH  Google Scholar 

  7. Nakagawa K, Kanaya F (1933) On the converse theorem in statistical hypothesis testing for Markov chains. IEEE Trans Inform Theory 39:629–633

    Article  MathSciNet  MATH  Google Scholar 

  8. Zhao SJ, Gao FQ (2010) Large deviations in testing Jacobi model. Stat Probab Lett 80:34–41

    Article  MathSciNet  MATH  Google Scholar 

  9. Gao FQ, Jiang H (2009) Moderate deviations for squared radial Ornstein-Uhlenbeck process. Stat Probab Lett 79:1378–1386

    Article  MATH  Google Scholar 

  10. Zani M (2002) Large deviations for squared radial Ornstein-Uhlenbeck processes. Stoch Process Appl 102:25–42

    Article  MathSciNet  MATH  Google Scholar 

  11. Watson GN (1995) A treatise on the theory of bessel function. Cambridge University Press Cambridge

    Google Scholar 

  12. Pitman J, Yor M (1982) A decomposition of Bessel bridges. Z Wahrscheinlichkeitstheor Verwandte Geb 59:425–457

    Google Scholar 

  13. Dembo A, Zeitouni O (1988) Large deviation technique and applications. Springer, New York

    MATH  Google Scholar 

Download references

Acknowledgments

We would like to express our gratitude to Prof. Gao F.Q., who help to improve the paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shou-Jiang Zhao .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chen, CP., Zhao, SJ., Liu, QJ. (2013). Hypothesis Testing for Squared Radial Ornstein–Uhleneck Model: Moderate Deviations Method. In: Yin, Z., Pan, L., Fang, X. (eds) Proceedings of The Eighth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA), 2013. Advances in Intelligent Systems and Computing, vol 212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37502-6_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-37502-6_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37501-9

  • Online ISBN: 978-3-642-37502-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics