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Some new tests for normality based on U-processes

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  • Arcones, Miguel A.
  • Wang, Yishi

Abstract

We present two new tests for normality based on U-processes. These tests improve on the Lilliefors tests. We obtain the consistency and asymptotic null distribution of these tests. We present simulations of the power of these tests and of several classical tests for some fixed alternatives. These simulations show that the presented tests are competitive.

Suggested Citation

  • Arcones, Miguel A. & Wang, Yishi, 2006. "Some new tests for normality based on U-processes," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 69-82, January.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:1:p:69-82
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    References listed on IDEAS

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    1. Truc Nguyen & Khoan Dinh, 2003. "Characterizations of normal distributions and EDF goodness-of-fit tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(2), pages 149-157, September.
    2. L. Baringhaus & N. Henze, 1988. "A consistent test for multivariate normality based on the empirical characteristic function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 35(1), pages 339-348, December.
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    Cited by:

    1. Kleijnen, J.P.C., 2007. "Simulation Experiments in Practice : Statistical Design and Regression Analysis," Discussion Paper 2007-09, Tilburg University, Center for Economic Research.
    2. Schick, Anton & Wang, Yishi & Wefelmeyer, Wolfgang, 2011. "Tests for normality based on density estimators of convolutions," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 337-343, February.
    3. Kleijnen, J.P.C., 2006. "White Noise Assumptions Revisited : Regression Models and Statistical Designs for Simulation Practice," Discussion Paper 2006-50, Tilburg University, Center for Economic Research.
    4. Salim Bouzebda & Amel Nezzal & Tarek Zari, 2022. "Uniform Consistency for Functional Conditional U -Statistics Using Delta-Sequences," Mathematics, MDPI, vol. 11(1), pages 1-39, December.
    5. Salim Bouzebda & Thouria El-hadjali & Anouar Abdeldjaoued Ferfache, 2023. "Uniform in Bandwidth Consistency of Conditional U-statistics Adaptive to Intrinsic Dimension in Presence of Censored Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1548-1606, August.
    6. Tenreiro, Carlos, 2009. "On the choice of the smoothing parameter for the BHEP goodness-of-fit test," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1038-1053, February.
    7. Christian Goldmann & Bernhard Klar & Simos Meintanis, 2015. "Data transformations and goodness-of-fit tests for type-II right censored samples," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(1), pages 59-83, January.
    8. Salim Bouzebda & Inass Soukarieh, 2022. "Non-Parametric Conditional U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 11(1), pages 1-69, December.
    9. Salim Bouzebda, 2024. "Limit Theorems in the Nonparametric Conditional Single-Index U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 12(13), pages 1-81, June.
    10. Salim Bouzebda & Boutheina Nemouchi, 2023. "Weak-convergence of empirical conditional processes and conditional U-processes involving functional mixing data," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 33-88, April.

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    Test of normality U-processes;

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