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Large deviations probabilities for a test of symmetry based on kernel density estimator


  • Osmoukhina, Anna V.


The goal is to prove large deviations limit theorems for statistics, which are based on kernel density estimator and which are designed for symmetry testing. The formulas for the rate functions of the pointwise difference and the uniform norm of the difference are expressed in terms of the underlying density function and their asymptotics are found.

Suggested Citation

  • Osmoukhina, Anna V., 2001. "Large deviations probabilities for a test of symmetry based on kernel density estimator," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 363-371, October.
  • Handle: RePEc:eee:stapro:v:54:y:2001:i:4:p:363-371

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    References listed on IDEAS

    1. Veraverbeke, N., 1977. "Asymptotic behaviour of Wiener-Hopf factors of a random walk," Stochastic Processes and their Applications, Elsevier, vol. 5(1), pages 27-37, February.
    2. Embrechts, Paul & Goldie, Charles M., 1982. "On convolution tails," Stochastic Processes and their Applications, Elsevier, vol. 13(3), pages 263-278, September.
    3. Sgibnev, M. S., 2001. "Exact asymptotic behaviour of the distribution of the supremum," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 301-311, April.
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    Cited by:

    1. Berrahou, Noureddine, 2008. "Large deviations probabilities for a symmetry test statistic based on delta-sequence density estimation," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 238-248, February.


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