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Empirical Hankel transforms and its applications to goodness-of-fit tests

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  • Baringhaus, Ludwig
  • Taherizadeh, Fatemeh

Abstract

We introduce a special Hankel transform for probability distributions on the nonnegative half-line and discuss some of its properties. Due to the uniqueness of the transform we suggest an integral type test statistic based on the empirical Hankel transform to treat simple and composite hypotheses goodness-of-fit problems. The special case of exponential distributions is studied in detail.

Suggested Citation

  • Baringhaus, Ludwig & Taherizadeh, Fatemeh, 2010. "Empirical Hankel transforms and its applications to goodness-of-fit tests," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1445-1457, July.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:6:p:1445-1457
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    References listed on IDEAS

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    1. Jiménez-Gamero, M.D. & Alba-Fernández, V. & Muñoz-García, J. & Chalco-Cano, Y., 2009. "Goodness-of-fit tests based on empirical characteristic functions," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 3957-3971, October.
    2. Norbert Henze & Simos G. Meintanis, 2005. "Recent and classical tests for exponentiality: a partial review with comparisons," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(1), pages 29-45, February.
    3. Meintanis, Simos & Swanepoel, Jan, 2007. "Bootstrap goodness-of-fit tests with estimated parameters based on empirical transforms," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 1004-1013, June.
    4. Ludwig Baringhaus & Norbert Henze, 1991. "A class of consistent tests for exponentiality based on the empirical Laplace transform," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(3), pages 551-564, September.
    5. Henze, Norbert & Wagner, Thorsten, 1997. "A New Approach to the BHEP Tests for Multivariate Normality," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 1-23, July.
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    Cited by:

    1. L. Baringhaus & D. Kolbe, 2015. "Two-sample tests based on empirical Hankel transforms," Statistical Papers, Springer, vol. 56(3), pages 597-617, August.
    2. Žikica Lukić & Bojana Milošević, 2024. "A novel two-sample test within the space of symmetric positive definite matrix distributions and its application in finance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 797-820, October.
    3. Elena Hadjicosta & Donald Richards, 2020. "Integral transform methods in goodness-of-fit testing, II: the Wishart distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1317-1370, December.

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