IDEAS home Printed from https://ideas.repec.org/a/taf/gnstxx/v22y2010i5p567-583.html
   My bibliography  Save this article

Bootstrapping the NPMLE for doubly truncated data

Author

Listed:
  • Carla Moreira
  • Jacobo de Uña-Álvarez

Abstract

Doubly truncated data appear in a number of applications, including astronomy and survival analysis. In this paper we review the existing methods to compute the nonparametric maximum likelihood estimator (NPMLE) under double truncation, which has no explicit form and must be approximated numerically. We introduce the bootstrap as a suitable method to estimate the finite sample distribution of the NPMLE under double truncation. The performance of the bootstrap is investigated in a simulation study. The nonstandard case in which the right- and left-truncation times determine each other is covered. As an illustration, nonparametric estimation and inference on the birth process and the age at diagnosis for childhood cancer in North Portugal is considered.

Suggested Citation

  • Carla Moreira & Jacobo de Uña-Álvarez, 2010. "Bootstrapping the NPMLE for doubly truncated data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 567-583.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:5:p:567-583
    DOI: 10.1080/10485250903556102
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/10485250903556102
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/10485250903556102?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mark Yuying An & Roberto Ayala, 1996. "Nonparametric Estimation of a Survivor Function with Across- Interval-Censored Data," Econometrics 9611003, University Library of Munich, Germany.
    2. van der Laan, Mark J., 1996. "Nonparametric Estimation of the Bivariate Survival Function with Truncated Data," Journal of Multivariate Analysis, Elsevier, vol. 58(1), pages 107-131, July.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pao-Sheng Shen, 2013. "A class of rank-based tests for doubly-truncated data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 83-102, March.
    2. Pao-sheng Shen & Yi Liu, 2019. "Pseudo maximum likelihood estimation for the Cox model with doubly truncated data," Statistical Papers, Springer, vol. 60(4), pages 1207-1224, August.
    3. Pao-Sheng Shen, 2011. "Testing quasi-independence for doubly truncated data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 753-761.
    4. Carla Moreira & Jacobo de Uña-Álvarez & Roel Braekers, 2021. "Nonparametric estimation of a distribution function from doubly truncated data under dependence," Computational Statistics, Springer, vol. 36(3), pages 1693-1720, September.
    5. Shen, Pao-sheng & Hsu, Huichen, 2020. "Conditional maximum likelihood estimation for semiparametric transformation models with doubly truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    6. Xiaohui Yuan & Huixian Li & Tianqing Liu, 2021. "Empirical likelihood inference for rank regression with doubly truncated data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 25-73, March.
    7. Achim Dörre & Chung-Yan Huang & Yi-Kuan Tseng & Takeshi Emura, 2021. "Likelihood-based analysis of doubly-truncated data under the location-scale and AFT model," Computational Statistics, Springer, vol. 36(1), pages 375-408, March.
    8. Kavita Sardana, 2021. "Double truncation in choice-based sample: An application of on-site survey sample," Economics Bulletin, AccessEcon, vol. 41(2), pages 781-787.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hongsheng Dai & Marialuisa Restaino & Huan Wang, 2016. "A class of nonparametric bivariate survival function estimators for randomly censored and truncated data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 736-751, October.
    2. Jeongyong Kim & Karen Bandeen-Roche, 2019. "Parametric estimation of association in bivariate failure-time data subject to competing risks: sensitivity to underlying assumptions," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(2), pages 259-279, April.
    3. Goele Massonnet & Paul Janssen & Tomasz Burzykowski, 2008. "Fitting Conditional Survival Models to Meta‐Analytic Data by Using a Transformation Toward Mixed‐Effects Models," Biometrics, The International Biometric Society, vol. 64(3), pages 834-842, September.
    4. 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.
    5. An, Mark Y. & Roberto Ayala, 1995. "A Mixture Model of Willingness to Pay Distributions," Working Papers 95-21, Duke University, Department of Economics.
    6. Shen, Pao-sheng, 2009. "An inverse-probability-weighted approach to the estimation of distribution function with doubly censored data," Statistics & Probability Letters, Elsevier, vol. 79(9), pages 1269-1276, May.
    7. José Sanz & Luis Herrero & Ana Bedate, 2003. "Contingent Valuation and Semiparametric Methods: A Case Study of the National Museum of Sculpture in Valladolid, Spain," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 27(3), pages 241-257, November.
    8. W. George Hutchinson & Riccardo Scarpa & Susan M. Chilton & T. McCallion, 2001. "Parametric and Non‐Parametric Estimates of Willingness to Pay for Forest Recreation in Northern Ireland: A Discrete Choice Contingent Valuation Study with Follow‐Ups," Journal of Agricultural Economics, Wiley Blackwell, vol. 52(1), pages 104-122, January.
    9. Shen, Pao-sheng, 2010. "Semiparametric estimation of survival function when data are subject to dependent censoring and left truncation," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 161-168, February.
    10. Xun, Li & Shao, Li & Zhou, Yong, 2017. "Efficiency of estimators for quantile differences with left truncated and right censored data," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 29-36.
    11. Pao-sheng Shen, 2010. "Nonparametric analysis of doubly truncated data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 835-853, October.
    12. Gürler, Ülkü & Prewitt, Kathryn, 2000. "Bivariate Density Estimation with Randomly Truncated Data," Journal of Multivariate Analysis, Elsevier, vol. 74(1), pages 88-115, July.
    13. An, Mark Yuying, 1996. "Semiparametric Estimation of Willingness to Pay Distributions," Working Papers 96-20, Duke University, Department of Economics.
    14. Jacobo de Uña‐Álvarez & Micha Mandel, 2018. "Nonparametric estimation of transition probabilities for a general progressive multi‐state model under cross‐sectional sampling," Biometrics, The International Biometric Society, vol. 74(4), pages 1203-1212, December.
    15. Mark Yuying An, 1996. "Statistical Inference of a Bivariate Proportional Hazard Model with Grouped Data," Econometrics 9611005, University Library of Munich, Germany.
    16. Brett Day, 2007. "Distribution-free estimation with interval-censored contingent valuation data: troubles with Turnbull?," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 37(4), pages 777-795, August.
    17. Daniel Rabinowitz & Qiong Yang, 1999. "Testing for Age-at-Onset Anticipation with Affected Parent-Child Pairs," Biometrics, The International Biometric Society, vol. 55(3), pages 834-838, September.
    18. Moreira, Carla & de Una-Alvarez, Jacobo & Van Keilegom, Ingrid, 2012. "Goodness-of-fit Tests for a Semiparametric Model under Random Double Truncation," LIDAM Discussion Papers ISBA 2012024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Chengbo Li & Yong Zhou, 2021. "The estimation for the general additive–multiplicative hazard model using the length-biased survival data," Statistical Papers, Springer, vol. 62(1), pages 53-74, February.
    20. Bella Vakulenko-Lagun & Micha Mandel & Yair Goldberg, 2017. "Nonparametric estimation in the illness-death model using prevalent data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(1), pages 25-56, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:gnstxx:v:22:y:2010:i:5:p:567-583. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/GNST20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.