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Relative density estimation for left truncated and right censored data

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  • Elisa–María Molanes-López
  • Ricardo Cao

Abstract

In biostatistical applications, it is very common that the generation of data is subject to mechanisms of loss of information such as censoring and truncation. In this setting, the direct application of traditional methods designed for completely observed data is not suitable at all. In the setting of a two-sample problem, this paper is focused on a kernel-type relative density estimator defined for left truncated and right censored data. First of all, an asymptotic representation of the estimator is found and based on this representation, its bias, variance and limit distribution are obtained. Then, a plug-in global bandwidth selector is designed for the kernel-type relative density estimator and their performance is checked through a simulation study. Finally, the estimator and the bandwidth selector are applied to a medical data set concerning gastric adenocarcinoma.

Suggested Citation

  • Elisa–María Molanes-López & Ricardo Cao, 2008. "Relative density estimation for left truncated and right censored data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(8), pages 693-720.
    • Handle: RePEc:taf:gnstxx:v:20:y:2008:i:8:p:693-720
    DOI: 10.1080/10485250802447882
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    References listed on IDEAS

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    1. Hall, Peter G. & Hyndman, Rob J., 2003. "Improved methods for bandwidth selection when estimating ROC curves," Statistics & Probability Letters, Elsevier, vol. 64(2), pages 181-189, August.
    2. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2006. "On the use of the bootstrap for estimating functions with functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1063-1074, November.
    3. Mark S. Handcock & Paul L. Janssen, 2002. "Statistical Inference for the Relative Density," Sociological Methods & Research, , vol. 30(3), pages 394-424, February.
    4. Cao, Ricardo & Janssen, Paul & Veraverbeke, Noel, 2001. "Relative density estimation and local bandwidth selection for censored data," Computational Statistics & Data Analysis, Elsevier, vol. 36(4), pages 497-510, June.
    5. Margaret Sullivan Pepe & Tianxi Cai, 2004. "The Analysis of Placement Values for Evaluating Discriminatory Measures," Biometrics, The International Biometric Society, vol. 60(2), pages 528-535, June.
    6. Cwik, Jan & Mielniczuk, Jan, 1993. "Data-dependent bandwidth choice for a grade density kernel estimate," Statistics & Probability Letters, Elsevier, vol. 16(5), pages 397-405, April.
    7. Lloyd, Chris J. & Yong, Zhou, 1999. "Kernel estimators of the ROC curve are better than empirical," Statistics & Probability Letters, Elsevier, vol. 44(3), pages 221-228, September.
    8. Chris J. Lloyd, 2000. "Regression Models for Convex ROC Curves," Biometrics, The International Biometric Society, vol. 56(3), pages 862-867, September.
    9. Ricardo Cao & Paul Janssen & Noël Veraverbeke, 2005. "Relative hazard rate estimation for right censored and left truncated data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 257-280, June.
    10. Lopez-Pintado, Sara & Romo, Juan, 2007. "Depth-based inference for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4957-4968, June.
    11. Gijbels, I. & Wang, J. L., 1993. "Strong Representations of the Survival Function Estimator for Truncated and Censored Data with Applications," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 210-229, November.
    12. Zhou, Yong & Yip, Paul S. F., 1999. "A Strong Representation of the Product-Limit Estimator for Left Truncated and Right Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 69(2), pages 261-280, May.
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    Cited by:

    1. Mnatsakanov, Robert M. & Pommeret, Denys, 2024. "On recovering the relative distribution, Part 1: The moment-recovered approach," Statistics & Probability Letters, Elsevier, vol. 208(C).

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