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Likelihood-based analysis of doubly-truncated data under the location-scale and AFT model

Author

Listed:
  • Achim Dörre

    (University of Rostock)

  • Chung-Yan Huang

    (National Central University)

  • Yi-Kuan Tseng

    (National Central University)

  • Takeshi Emura

    (Chang Gung University)

Abstract

Doubly-truncated data arise in many fields, including economics, engineering, medicine, and astronomy. This article develops likelihood-based inference methods for lifetime distributions under the log-location-scale model and the accelerated failure time model based on doubly-truncated data. These parametric models are practically useful, but the methodologies to fit these models to doubly-truncated data are missing. We develop algorithms for obtaining the maximum likelihood estimator under both models, and propose several types of interval estimation methods. Furthermore, we show that the confidence band for the cumulative distribution function has closed-form expressions. We conduct simulations to examine the accuracy of the proposed methods. We illustrate our proposed methods by real data from a field reliability study, called the Equipment-S data.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:1:d:10.1007_s00180-020-01027-6
    DOI: 10.1007/s00180-020-01027-6
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    References listed on IDEAS

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    1. Moreira, Carla & Van Keilegom, Ingrid, 2013. "Bandwidth selection for kernel density estimation with doubly truncated data," LIDAM Reprints ISBA 2013018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Takeshi Emura & Yoshihiko Konno, 2012. "Multivariate normal distribution approaches for dependently truncated data," Statistical Papers, Springer, vol. 53(1), pages 133-149, February.
    3. 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.
    4. Carla Moreira & Jacobo Uña-Álvarez & Ingrid Keilegom, 2014. "Goodness-of-fit tests for a semiparametric model under random double truncation," Computational Statistics, Springer, vol. 29(5), pages 1365-1379, October.
    5. Moreira, C. & Van Keilegom, I., 2013. "Bandwidth selection for kernel density estimation with doubly truncated data," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 107-123.
    6. Takeshi Emura & Ya-Hsuan Hu & Yoshihiko Konno, 2017. "Asymptotic inference for maximum likelihood estimators under the special exponential family with double-truncation," Statistical Papers, Springer, vol. 58(3), pages 877-909, September.
    7. Takeshi Emura & Chi-Hung Pan, 2020. "Parametric likelihood inference and goodness-of-fit for dependently left-truncated data, a copula-based approach," Statistical Papers, Springer, vol. 61(1), pages 479-501, February.
    8. P. Sankaran & S. Sunoj, 2004. "Identification of models using failure rate and mean residual life of doubly truncated random variables," Statistical Papers, Springer, vol. 45(1), pages 97-109, January.
    9. Pao-Sheng Shen, 2011. "Testing quasi-independence for doubly truncated data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 753-761.
    10. 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.
    11. Ya-Hsuan Hu & Takeshi Emura, 2015. "Maximum likelihood estimation for a special exponential family under random double-truncation," Computational Statistics, Springer, vol. 30(4), pages 1199-1229, December.
    12. Moreira, Carla & de Una-Alvarez, Jacobo & Van Keilegom, Ingrid, 2014. "Goodness-of-fit tests for a semiparametric model under random double truncation," LIDAM Reprints ISBA 2014039, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    Cited by:

    1. Hirofumi Michimae & Takeshi Emura, 2022. "Likelihood Inference for Copula Models Based on Left-Truncated and Competing Risks Data from Field Studies," Mathematics, MDPI, vol. 10(13), pages 1-15, June.
    2. Nanami Taketomi & Kazuki Yamamoto & Christophe Chesneau & Takeshi Emura, 2022. "Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch," Mathematics, MDPI, vol. 10(20), pages 1-23, October.

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