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Strassen's LIL for the Lorenz Curve

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  • Csörgo, Miklós
  • Zitikis, Ricardas

Abstract

We prove Strassen's law of the iterated logarithm for the Lorenz process assuming that the underlying distribution functionFand its inverseF-1are continuous, and the momentEX2+[var epsilon]is finite for some[var epsilon]>0. Previous work in this area is based on assuming the existence of the densityf:=F' combined with further assumptions onFandf. Being based only on continuity and moment assumptions, our method of proof is different from that used previously by others, and is mainly based on a limit theorem for the (general) integrated empirical difference process. The obtained result covers all those we are aware of on the LIL problem in this area.

Suggested Citation

  • Csörgo, Miklós & Zitikis, Ricardas, 1996. "Strassen's LIL for the Lorenz Curve," Journal of Multivariate Analysis, Elsevier, vol. 59(1), pages 1-12, October.
  • Handle: RePEc:eee:jmvana:v:59:y:1996:i:1:p:1-12
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    References listed on IDEAS

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    1. Dielman, Terry E. & Rose, Elizabeth L., 1996. "A note on hypothesis testing in LAV multiple regression: A small sample comparison," Computational Statistics & Data Analysis, Elsevier, vol. 21(4), pages 463-470, April.
    2. Dielman, Terry E. & Rose, Elizabeth L., 1995. "A bootstrap approach to hypothesis testing in least absolute value regression," Computational Statistics & Data Analysis, Elsevier, vol. 20(2), pages 119-130, August.
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    Citations

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    Cited by:

    1. Csörgö, Miklós & Zitikis, Ricardas, 1997. "On the rate of strong consistency of Lorenz curves," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 113-121, June.
    2. Csörgo, Miklós & Zitikis, Ricardas, 1998. "On the Rate of Strong Consistency of the Total Time on Test Statistic," Journal of Multivariate Analysis, Elsevier, vol. 66(1), pages 99-117, July.
    3. Tse, SzeMan, 2011. "Composing the cumulative quantile regression function and the Goldie concentration curve," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 674-682, March.
    4. Csörgo, Miklós & Zitikis, Ricardas, 2001. "The Vervaat Process in Lp Spaces," Journal of Multivariate Analysis, Elsevier, vol. 78(1), pages 103-138, July.
    5. Fakoor, V. & Ghalibaf, M. Bolbolian & Azarnoosh, H.A., 2011. "Asymptotic behaviors of the Lorenz curve and Gini index in sampling from a length-biased distribution," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1425-1435, September.

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