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Tests for normality based on density estimators of convolutions

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  • Schick, Anton
  • Wang, Yishi
  • Wefelmeyer, Wolfgang

Abstract

Recent results show that densities of convolutions can be estimated by local U-statistics at the root-n rate in various norms. Motivated by this and the fact that convolutions of normal densities are normal, we introduce new tests for normality which use as test statistics weighted L1-distances between the standard normal density and local U-statistics based on standardized observations. We show that such test statistics converge at the root-n rate and determine their limit distributions as functionals of Gaussian processes. We also address a choice of bandwidth. Simulations show that our tests are competitive with other tests of normality.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:2:p:337-343
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    References listed on IDEAS

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    1. 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.
    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. 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.
    2. Norbert Henze & Stefan Koch, 2020. "On a test of normality based on the empirical moment generating function," Statistical Papers, Springer, vol. 61(1), pages 17-29, February.
    3. 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.
    4. Inass Soukarieh & Salim Bouzebda, 2022. "Exchangeably Weighted Bootstraps of General Markov U -Process," Mathematics, MDPI, vol. 10(20), pages 1-42, October.

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