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Strong representation of a conditional quantile function estimator with truncated and censored data

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  • Iglesias-Pérez, M. C.

Abstract

We consider lifetime data with covariables which are subject to both left truncation and right censorship. In this context, it is interesting to study the conditional distribution function of the lifetime and the corresponding conditional quantile function. A generalized product-limit estimator (GPLE) of the conditional distribution function has been studied in Iglesias-Pérez and González-Manteiga (J. Nonparametric Statist. 10 (1999) 213). In the present paper, we define a conditional quantile function estimator via the mentioned GPLE and we derive an almost sure representation for this quantile estimator. This result extends strong quantile representations studied on conditional survival analysis for censored data (Dabrowska (Sankhya Ser. A 54 (1992) 252) and Van Keilegom and Veraverbeke (J. Statist. Plann. Inference 69 (1998) 115)). As consequence of this representation we establish the asymptotic normality of the conditional quantile estimator.

Suggested Citation

  • Iglesias-Pérez, M. C., 2003. "Strong representation of a conditional quantile function estimator with truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 65(2), pages 79-91, November.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:2:p:79-91
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    References listed on IDEAS

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    1. Gürler, Ülkü & Stute, Winfried & Wang, Jane-Ling, 1993. "Weak and strong quantile representations for randomly truncated data with applications," Statistics & Probability Letters, Elsevier, vol. 17(2), pages 139-148, May.
    2. Zhou, Yong, 1996. "A note on the TJW product-limit estimator for truncated and censored data," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 381-387, March.
    3. M. Iglesias Pérez & W. González Manteiga, 2003. "Bootstrap for the conditional distribution function with truncated and censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 331-357, June.
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    1. Han-Ying Liang & Jacobo Uña-Álvarez, 2011. "Asymptotic properties of conditional quantile estimator for censored dependent observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 267-289, April.

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