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Large deviations for L-statistics

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  • Boistard Hélène

Abstract

The purpose of this paper is to establish a functional large deviations principle (LDP) for L-statistics under some new tail conditions. The method is based on Sanov's theorem and on basic tools of large deviations theory. Our study includes a full treatment of the case of the uniform law and an example in which the rate function can be calculated very precisely. We extend our result by an LDP for normalized L-statistics. The case of the exponential distribution, which is not in the scope of the previous conditions, is completely treated with another method. We provide a functional LDP obtained via Gärtner–Ellis theorem.

Suggested Citation

  • Boistard Hélène, 2007. "Large deviations for L-statistics," Statistics & Risk Modeling, De Gruyter, vol. 25(2/2007), pages 1-37, April.
    • Handle: RePEc:bpj:strimo:v:25:y:2007:i:2/2007:p:37:n:3
    DOI: 10.1524/stnd.2007.25.2.89
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    References listed on IDEAS

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    1. Gamboa, F. & Rouault, A. & Zani, M., 1999. "A functional large deviations principle for quadratic forms of Gaussian stationary processes," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 299-308, July.
    2. Li, Deli & Bhaskara Rao, M. & Tomkins, R. J., 2001. "The Law of the Iterated Logarithm and Central Limit Theorem for L-Statistics," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 191-217, August.
    3. Eustasio Barrio & Juan Cuesta-Albertos & Carlos Matrán & Sándor Csörgö & Carles Cuadras & Tertius Wet & Evarist Giné & Richard Lockhart & Axel Munk & Winfried Stute, 2000. "Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(1), pages 1-96, June.
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