IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v61y2020i3d10.1007_s00362-017-0968-7.html
   My bibliography  Save this article

Bayesian estimation of a lifetime distribution under double truncation caused by time-restricted data collection

Author

Listed:
  • Achim Dörre

    (University of Rostock)

Abstract

We study a type of double truncation where units are observed if and only if their death event occurs within a specific timespan. The resulting missing data mechanism is nonignorable and thus has to be reconsidered. Based on the density function of observed lifetimes and the random sample size, we derive a likelihood model that enables simultaneous estimation of the lifetime distribution and the parameters governing the birth process. In particular, knowledge of the population size is not required. We show that the model is identifiable under certain conditions by using results on exponential families. Bayesian estimators and corresponding standard errors for all involved parameters become available by using MCMC simulation. We describe how the simulation can be performed efficiently while maintaining sufficiently good mixing behaviour of the resulting chains. Both finite-sample and asymptotic properties of the investigated estimators are examined through a simulation study. The proposed method is applied to estimate the lifetime distribution of German companies.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:3:d:10.1007_s00362-017-0968-7
    DOI: 10.1007/s00362-017-0968-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-017-0968-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-017-0968-7?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. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521477444, January.
    2. Han-Ying Liang & Jong-Il Baek, 2016. "Asymptotic normality of conditional density estimation with left-truncated and dependent data," Statistical Papers, Springer, vol. 57(1), pages 1-20, March.
    3. Lee J. & Berger J.O., 2001. "Semiparametric Bayesian Analysis of Selection Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1397-1409, December.
    4. Takeshi Emura & Yoshihiko Konno, 2012. "Multivariate normal distribution approaches for dependently truncated data," Statistical Papers, Springer, vol. 53(1), pages 133-149, February.
    5. 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.
    6. 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.
    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. Mengyue Zhang & Shishun Zhao & Tao Hu & Da Xu & Jianguo Sun, 2023. "Regression Analysis of Dependent Current Status Data with Left Truncation," Mathematics, MDPI, vol. 11(16), pages 1-13, August.

    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. 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).
    4. Aboubacar Amiri & Baba Thiam, 2018. "Regression estimation by local polynomial fitting for multivariate data streams," Statistical Papers, Springer, vol. 59(2), pages 813-843, June.
    5. Bo E. Honoré & Luojia Hu, 2023. "The COVID-19 pandemic and Asian American employment," Empirical Economics, Springer, vol. 64(5), pages 2053-2083, May.
    6. Georgiev, Iliyan, 2010. "Model-based asymptotic inference on the effect of infrequent large shocks on cointegrated variables," Journal of Econometrics, Elsevier, vol. 158(1), pages 37-50, September.
    7. Patrick Gagliardini & Christian Gouriéroux, 2011. "Approximate Derivative Pricing for Large Classes of Homogeneous Assets with Systematic Risk," Journal of Financial Econometrics, Oxford University Press, vol. 9(2), pages 237-280, Spring.
    8. Bergman, Mats A. & Johansson, Per & Bergman, M.A., 2002. "Large investments in the pulp and paper industry: a count data regression analysis," Journal of Forest Economics, Elsevier, vol. 8(1), pages 29-52.
    9. Luis Orea & David Roibás & Alan Wall, 2004. "Choosing the Technical Efficiency Orientation to Analyze Firms' Technology: A Model Selection Test Approach," Journal of Productivity Analysis, Springer, vol. 22(1), pages 51-71, July.
    10. Gerhard, Frank & Hess, Dieter & Pohlmeier, Winfried, 1998. "What a Difference a Day Makes: On the Common Market Microstructure of Trading Days," CoFE Discussion Papers 98/01, University of Konstanz, Center of Finance and Econometrics (CoFE).
    11. Alexandre Petkovic & David Veredas, 2009. "Aggregation of linear models for panel data," Working Papers ECARES 2009-012, ULB -- Universite Libre de Bruxelles.
    12. 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.
    13. Heng Chen & Daniel F. Heitjan, 2022. "Analysis of local sensitivity to nonignorability with missing outcomes and predictors," Biometrics, The International Biometric Society, vol. 78(4), pages 1342-1352, December.
    14. Roxana Chiriac & Valeri Voev, 2011. "Modelling and forecasting multivariate realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(6), pages 922-947, September.
    15. Mirjam van Praag & Arvid Raknerud, 2021. "The Returns to Entrepreneurship: Evidence from Matched Person-firm Data," Research in Labor Economics, in: Workplace Productivity and Management Practices, volume 49, pages 207-238, Emerald Group Publishing Limited.
    16. Zhongqi Liang & Qihua Wang & Yuting Wei, 2022. "Robust model selection with covariables missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 539-557, June.
    17. Sun, Yixiao X & Phillips, Peter C. B. & Jin, Sainan, 2005. "Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing∗," University of California at San Diego, Economics Working Paper Series qt16b3j2hd, Department of Economics, UC San Diego.
    18. Laurent, Sébastien & Rombouts, Jeroen V.K. & Violante, Francesco, 2013. "On loss functions and ranking forecasting performances of multivariate volatility models," Journal of Econometrics, Elsevier, vol. 173(1), pages 1-10.
    19. van den Berg, Gerard J. & van der Klaauw, Bas, 2001. "Combining micro and macro unemployment duration data," Journal of Econometrics, Elsevier, vol. 102(2), pages 271-309, June.
    20. Boug, Pål & Cappelen, Adne & Swensen, Anders Rygh, 2010. "The new Keynesian Phillips curve revisited," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 858-874, May.

    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:stpapr:v:61:y:2020:i:3:d:10.1007_s00362-017-0968-7. 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.