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Maximum likelihood estimation for a special exponential family under random double-truncation

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  • Ya-Hsuan Hu
  • Takeshi Emura

Abstract

Doubly-truncated data often appear in lifetime data analysis, where samples are collected under certain time constraints. Nonparametric methods for doubly-truncated data have been studied well in the literature. Alternatively, this paper considers parametric inference when samples are subject to double-truncation. Efron and Petrosian (J Am Stat Assoc 94:824–834, 1999 ) proposed to fit a parametric family, called the special exponential family, with doubly-truncated data. However, non-trivial technical aspects, such as parameter space, support of the density, and computational algorithms, have not been discussed in the literature. This paper fills this gap by providing the technical aspects, including adequate choices of parameter space as well as support, and reliable computational algorithms. Simulations are conducted to verify the suggested techniques, and real data are used for illustration. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:30:y:2015:i:4:p:1199-1229
    DOI: 10.1007/s00180-015-0564-z
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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. 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.
    3. Henry T Robertson & David B Allison, 2012. "A Novel Generalized Normal Distribution for Human Longevity and other Negatively Skewed Data," PLOS ONE, Public Library of Science, vol. 7(5), pages 1-7, May.
    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. 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.
    7. Joan Castillo, 1994. "The singly truncated normal distribution: A non-steep exponential family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(1), pages 57-66, March.
    8. Winfried Stute & Wenceslao Manteiga & Manuel Quindimil, 1993. "Bootstrap based goodness-of-fit-tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 243-256, December.
    9. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    10. Yi-Hau Chen, 2009. "Weighted Breslow-type and maximum likelihood estimation in semiparametric transformation models," Biometrika, Biometrika Trust, vol. 96(3), pages 591-600.
    11. Long, Ting-Hsuan & Emura, Takeshi, 2014. "A control chart using copula-based Markov chain models," MPRA Paper 57419, University Library of Munich, Germany.
    12. Hong Zhu & Mei-Cheng Wang, 2012. "Analysing bivariate survival data with interval sampling and application to cancer epidemiology," Biometrika, Biometrika Trust, vol. 99(2), pages 345-361.
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    Cited by:

    1. 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.
    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. Jia-Han Shih & Takeshi Emura, 2018. "Likelihood-based inference for bivariate latent failure time models with competing risks under the generalized FGM copula," Computational Statistics, Springer, vol. 33(3), pages 1293-1323, September.
    4. Achim Dörre, 2020. "Bayesian estimation of a lifetime distribution under double truncation caused by time-restricted data collection," Statistical Papers, Springer, vol. 61(3), pages 945-965, June.
    5. 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.
    6. 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).
    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.

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