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Strong approximations of the quantile process of the product-limit estimator

Author

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  • Aly, Emad-Eldin A. A.
  • Csörgo, Miklós
  • Horváth, Lajos

Abstract

The quantile process of the product-limit estimator (PL-quantile process) in the random censorship model from the right is studied via strong approximation methods. Some almost sure fluctuation properties of the said process are studied. Sections 3 and 4 contain strong approximations of the PL-quantile process by a generalized Kiefer process. The PL and PL-quantile processes by the same appropriate Kiefer process are approximated and it is demonstrated that this simultaneous approximation cannot be improved in general. Section 5 contains functional LIL for the PL-quantile process and also three methods of constructing confidence bands for theoretical quantiles in the random censorship model from the right.

Suggested Citation

  • Aly, Emad-Eldin A. A. & Csörgo, Miklós & Horváth, Lajos, 1985. "Strong approximations of the quantile process of the product-limit estimator," Journal of Multivariate Analysis, Elsevier, vol. 16(2), pages 185-210, April.
    • Handle: RePEc:eee:jmvana:v:16:y:1985:i:2:p:185-210
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    Cited by:

    1. J. Ghorai, 1991. "Estimation of a smooth quantile function under the proportional hazards model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(4), pages 747-760, December.
    2. Szeman Tse, 2005. "Quantile process for left truncated and right censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 61-69, March.
    3. Cheng, Cheng, 2002. "Almost-sure uniform error bounds of general smooth estimators of quantile density functions," Statistics & Probability Letters, Elsevier, vol. 59(2), pages 183-194, September.
    4. Janssen, Paul & Swanepoel, Jan & Veraverbeke, Noël, 2002. "The modified bootstrap error process for Kaplan-Meier quantiles," Statistics & Probability Letters, Elsevier, vol. 58(1), pages 31-39, May.

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