IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v30y2015i4p1199-1229.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00180-015-0564-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00180-015-0564-z?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. 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.
    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. 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. Yunhan Liu & Changchun Gao & Xiaofeng Liu & Ping Luo & Jianguo Ren, 2024. "A Comparison of MLE for Some Index Distributions Based on Censored Samples," Mathematics, MDPI, vol. 12(20), pages 1-15, October.
    4. 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.
    5. 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.
    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. 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).
    8. 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.

    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. 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.
    2. 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.
    3. 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.
    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. Anastasiou, Andreas, 2017. "Bounds for the normal approximation of the maximum likelihood estimator from m-dependent random variables," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 171-181.
    6. Antonio Di Crescenzo & Abdolsaeed Toomaj, 2022. "Weighted Mean Inactivity Time Function with Applications," Mathematics, MDPI, vol. 10(16), pages 1-30, August.
    7. Denter, Philipp & Sisak, Dana, 2015. "Do polls create momentum in political competition?," Journal of Public Economics, Elsevier, vol. 130(C), pages 1-14.
    8. Salgado Alfredo, 2018. "Incomplete Information and Costly Signaling in College Admissions," Working Papers 2018-23, Banco de México.
    9. Albrecht, James & Anderson, Axel & Vroman, Susan, 2010. "Search by committee," Journal of Economic Theory, Elsevier, vol. 145(4), pages 1386-1407, July.
    10. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    11. Chyong-Mei Chen & Pao-sheng Shen & Yi Liu, 2021. "On semiparametric transformation model with LTRC data: pseudo likelihood approach," Statistical Papers, Springer, vol. 62(1), pages 3-30, February.
    12. Simon Bruhn & Thomas Grebel & Lionel Nesta, 2023. "The fallacy in productivity decomposition," Journal of Evolutionary Economics, Springer, vol. 33(3), pages 797-835, July.
    13. Arthur Pewsey, 2018. "Parametric bootstrap edf-based goodness-of-fit testing for sinh–arcsinh distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 147-172, March.
    14. David de la Croix & Omar Licandro, 2015. "The longevity of famous people from Hammurabi to Einstein," Journal of Economic Growth, Springer, vol. 20(3), pages 263-303, September.
    15. Wim J. van der Linden, 2019. "Lord’s Equity Theorem Revisited," Journal of Educational and Behavioral Statistics, , vol. 44(4), pages 415-430, August.
    16. Joan Del Castillo & Marta Pérez-Casany, 1998. "Weighted Poisson Distributions for Overdispersion and Underdispersion Situations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(3), pages 567-585, September.
    17. Lee, Sangyeol & Oh, Haejune, 2015. "Entropy test and residual empirical process for autoregressive conditional duration models," Computational Statistics & Data Analysis, Elsevier, vol. 86(C), pages 1-12.
    18. Simar, Léopold & Wilson, Paul, 2022. "Modern Tools for Evaluating the Performance of Health-Care Providers," LIDAM Discussion Papers ISBA 2022006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Baey, Charlotte & Didier, Anne & Lemaire, Sébastien & Maupas, Fabienne & Cournède, Paul-Henry, 2013. "Modelling the interindividual variability of organogenesis in sugar beet populations using a hierarchical segmented model," Ecological Modelling, Elsevier, vol. 263(C), pages 56-63.
    20. Zacharias Psaradakis & Marián Vávra, 2017. "Normality Tests for Dependent Data: Large-Sample and Bootstrap Approaches," Birkbeck Working Papers in Economics and Finance 1706, Birkbeck, Department of Economics, Mathematics & 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:spr:compst:v:30:y:2015:i:4:p:1199-1229. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.