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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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    Cited by:

    1. 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.
    2. 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).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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    8. 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.

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