Skip to main content
SpringerLink
Log in

Strongly Consistent Detection for Nonparametric Hypotheses

  • Chapter
  • First Online:
Measures of Complexity

Abstract

Consider two robust detection problems formulated by nonparametric hypotheses such that both hypotheses are composite and indistinguishable. Strongly consistent testing rules are shown.

The research reported here was supported in part by the National Development Agency (NFÜ, Hungary) as part of the project Introduction of Cognitive Methods for UAV Collision Avoidance Using Millimeter Wave Radar (grant no.: KMR-12-1-2012-0008).

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

  1. Barron, A.R.: Uniformly powerful goodness of fit tests. Ann. Stat. 17(1), 107–124 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  2. Beirlant, J., Devroye, L., Györfi, L., Vajda, I.: Large deviations of divergence measures on partitions. J. Stat. Plan. Inference 93(1–2), 1–16 (2001)

    Article  MATH  Google Scholar 

  3. Biau, G., Györfi, L.: On the asymptotic properties of a nonparametric \(l_1\)-test statistic of homogeneity. IEEE Trans. Inf. Theory 51(11), 3965–3973 (2005)

    Article  MATH  Google Scholar 

  4. Darling, D.A., Robbins, H.: Some nonparametric sequential tests with power one. Proc. Natl. Acad. Sci. USA 61(3), 804–809 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dembo, A., Peres, Y.: A topological criterion for hypothesis testing. Ann. Stat. 22(1), 106–117 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  6. Devroye, L., Györfi, L.: Nonparametric Density Estimation: The \(L_1\) View. Wiley, New York (1985)

    Google Scholar 

  7. Devroye, L., Lugosi, G.: Almost sure classification of densities. J. Nonparametric Stat. 14(6), 675–698 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Devroye, L., Györfi, L., Lugosi, G.: A note on robust hypothesis testing. IEEE Trans. Inf. Theory 48(7), 2111–2114 (2002)

    Article  MATH  Google Scholar 

  9. Ermakov, M.: On distinguishability of hypotheses. Technical report (2013). arXiv:1308.4295

  10. Gretton, A., Györfi, L.: Consistent nonparametric tests of independence. J. Mach. Learn. Res. 11, 1391–1423 (2010)

    MathSciNet  MATH  Google Scholar 

  11. Györfi, L., Györfi, Z., Vajda, I.: A strong law of large numbers and some applications. Stud. Sci. Math. Hung. 12, 233–244 (1977)

    MATH  Google Scholar 

  12. Györfi, L., Kohler, M., Krzyżak, A., Walk, H.: Distribution-Free Theory of Nonparametric Regression. Springer, New York (2002)

    Book  MATH  Google Scholar 

  13. Györfi, L., Masry, E.: The \(L_1\) and \(L_2\) strong consistency of recursive kernel density estimation from dependent samples. IEEE Trans. Inf. Theory 36(3), 531–539 (1990)

    Article  MATH  Google Scholar 

  14. Györfi, L., van der Meulen, E.C.: A consistent goodness of fit test based on the total variation distance. In: Roussas, G. (ed.) Nonparametric Functional Estimation and Related Topics, pp. 631–645. Kluwer, Dordrecht (1990)

    Google Scholar 

  15. Györfi, L., Walk, H.: Strongly consistent nonparametric tests of conditional independence. Stat. Probab. Lett. 82(6), 1145–1150 (2012)

    Article  MATH  Google Scholar 

  16. Hoeffding, W.: Probability inequalities for sums of bounded random variables. J. Am. Stat. Assoc. 58(301), 13–30 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hoeffding, W., Wolfowitz, J.: Distinguishability of sets of distributions. Ann. Math. Stat. 29(3), 700–718 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  18. Kraft, C.: Some conditions for consistency and uniform consistency of statistical procedures. Univ. Calif. Publ. Stat. 2, 125–142 (1955)

    MathSciNet  Google Scholar 

  19. Le Cam, L.: Convergence of estimates under dimensionality restrictions. Ann. Stat. 1(1), 38–53 (1973)

    Article  MATH  Google Scholar 

  20. Le Cam, L., Schwartz, L.: A necessary and sufficient condition for the existence of consistent estimates. Ann. Math. Stat. 31(1), 140–150 (1960)

    Article  MATH  Google Scholar 

  21. Robbins, H.: Statistical methods related to the law of the iterated logarithm. Ann. Math. Stat. 41(5), 1397–1409 (1970)

    Article  MATH  Google Scholar 

  22. Scheffé, H.: A useful convergence theorem for probability distributions. Ann. Math. Stat. 18(3), 434–438 (1947)

    Article  MATH  Google Scholar 

  23. Schwartz, L.: On Bayes procedures. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 4(1), 10–26 (1965)

    Article  MATH  Google Scholar 

  24. Sen, P.K.: Sequential Nonparametrics: Invariance Principles and Statistical Inference. Wiley, New York (1981)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Stoczek u. 2, Budapest, 1521, Hungary

    László Györfi

  2. Department of Mathematics, University of Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Harro Walk

Authors
  1. László Györfi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Harro Walk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to László Györfi .

Editor information

Editors and Affiliations

  1. Dept. of Computer Science, Royal Holloway, Univ of London, Egham, Surrey, United Kingdom

    Vladimir Vovk

  2. Frederick University, Nicosia, Cyprus

    Harris Papadopoulos

  3. Dept. of Computer Science, University of London, Egham, Surrey, United Kingdom

    Alexander Gammerman

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Györfi, L., Walk, H. (2015). Strongly Consistent Detection for Nonparametric Hypotheses. In: Vovk, V., Papadopoulos, H., Gammerman, A. (eds) Measures of Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-21852-6_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-21852-6_22

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21851-9

  • Online ISBN: 978-3-319-21852-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation