IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v61y2020i6d10.1007_s00362-018-01064-w.html
   My bibliography  Save this article

The asymptotic properties for the estimators of the survival function and failure rate function based on WOD samples

Author

Listed:
  • Aiting Shen

    (Anhui University)

  • Huiling Tao

    (Anhui University)

  • Xuejun Wang

    (Anhui University)

Abstract

In this paper, the consistency for the estimators of the survival function and failure rate function in reliability theory is investigated. The strong consistency and the convergence rate for the estimators of the survival function and failure rate function based on widely orthant dependent (WOD, in short) samples are established. Our results established in the paper generalize the corresponding ones for independent samples and some negatively dependent samples.

Suggested Citation

  • Aiting Shen & Huiling Tao & Xuejun Wang, 2020. "The asymptotic properties for the estimators of the survival function and failure rate function based on WOD samples," Statistical Papers, Springer, vol. 61(6), pages 2671-2684, December.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:6:d:10.1007_s00362-018-01064-w
    DOI: 10.1007/s00362-018-01064-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-018-01064-w
    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/s00362-018-01064-w?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. Xuejun Wang & Chen Xu & Tien-Chung Hu & Andrei Volodin & Shuhe Hu, 2014. "On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 607-629, September.
    2. Aiting Shen, 2013. "Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, July.
    3. Liu, Xijun & Gao, Qingwu & Wang, Yuebao, 2012. "A note on a dependent risk model with constant interest rate," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 707-712.
    4. Kaiyong Wang & Yuebao Wang & Qingwu Gao, 2013. "Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 109-124, March.
    5. Boente, Graciela & Fraiman, Ricardo, 1988. "Consistency of a nonparametric estimate of a density function for dependent variables," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 90-99, April.
    6. He, Wei & Cheng, Dongya & Wang, Yuebao, 2013. "Asymptotic lower bounds of precise large deviations with nonnegative and dependent random variables," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 331-338.
    Full references (including those not matched with items on IDEAS)

    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. Xin Deng & Xuejun Wang, 2018. "Asymptotic Property of M Estimator in Classical Linear Models Under Dependent Random Errors," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1069-1090, December.
    2. Xin Deng & Xuejun Wang, 2020. "An exponential inequality and its application to M estimators in multiple linear models," Statistical Papers, Springer, vol. 61(4), pages 1607-1627, August.
    3. Xuejun Wang & Xin Deng & Shuhe Hu, 2018. "On consistency of the weighted least squares estimators in a semiparametric regression model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 797-820, October.
    4. Yi Wu & Xuejun Wang & Aiting Shen, 2023. "Strong Convergence for Weighted Sums of Widely Orthant Dependent Random Variables and Applications," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-28, March.
    5. Mengmei Xi & Rui Wang & Zhaoyang Cheng & Xuejun Wang, 2020. "Some convergence properties for partial sums of widely orthant dependent random variables and their statistical applications," Statistical Papers, Springer, vol. 61(4), pages 1663-1684, August.
    6. Xuejun Wang & Chen Xu & Tien-Chung Hu & Andrei Volodin & Shuhe Hu, 2014. "On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 607-629, September.
    7. Yi Wu & Wei Yu & Xuejun Wang, 2022. "Strong representations of the Kaplan–Meier estimator and hazard estimator with censored widely orthant dependent data," Computational Statistics, Springer, vol. 37(1), pages 383-402, March.
    8. Gao, Qingwu & Lin, Jia’nan & Liu, Xijun, 2023. "Large deviations of aggregate amount of claims in compound risk model with arbitrary dependence between claim sizes and waiting times," Statistics & Probability Letters, Elsevier, vol. 197(C).
    9. Jiang, Tao & Wang, Yuebao & Chen, Yang & Xu, Hui, 2015. "Uniform asymptotic estimate for finite-time ruin probabilities of a time-dependent bidimensional renewal model," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 45-53.
    10. Gao, Qingwu & Liu, Xijun, 2013. "Uniform asymptotics for the finite-time ruin probability with upper tail asymptotically independent claims and constant force of interest," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1527-1538.
    11. Yang Yang & Xinzhi Wang & Xiaonan Su & Aili Zhang, 2019. "Asymptotic Behavior of Ruin Probabilities in an Insurance Risk Model with Quasi-Asymptotically Independent or Bivariate Regularly Varying-Tailed Main Claim and By-Claim," Complexity, Hindawi, vol. 2019, pages 1-6, October.
    12. Chen, Pingyan & Sung, Soo Hak, 2019. "A Spitzer-type law of large numbers for widely orthant dependent random variables," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    13. Hongyan Fang & Saisai Ding & Xiaoqin Li & Wenzhi Yang, 2020. "Asymptotic Approximations of Ratio Moments Based on Dependent Sequences," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    14. Hongmin Xiao & Lin Xie, 2018. "Asymptotic Ruin Probability of a Bidimensional Risk Model Based on Entrance Processes with Constant Interest Rate," Risks, MDPI, vol. 6(4), pages 1-12, November.
    15. Labrador, Boris, 2008. "Strong pointwise consistency of the kT -occupation time density estimator," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1128-1137, July.
    16. Hallin, Marc & Lu, Zudi & Tran, Lanh T., 2004. "Kernel density estimation for spatial processes: the L1 theory," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 61-75, January.
    17. Jin Yu Zhou & Ji Gao Yan & Fei Du, 2023. "Complete and Complete f -Moment Convergence for Arrays of Rowwise END Random Variables and Some Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1307-1330, August.
    18. Lu, Zudi & Chen, Xing, 2004. "Spatial kernel regression estimation: weak consistency," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 125-136, June.
    19. Edita Kizinevič & Jonas Šiaulys, 2018. "The Exponential Estimate of the Ultimate Ruin Probability for the Non-Homogeneous Renewal Risk Model," Risks, MDPI, vol. 6(1), pages 1-17, March.
    20. Chu, Ba & Huynh, Kim & Jacho-Chavez, David, 2013. "Functionals of order statistics and their multivariate concomitants with application to semiparametric estimation by nearest neighbours," MPRA Paper 79670, University Library of Munich, Germany, revised 2012.

    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:6:d:10.1007_s00362-018-01064-w. 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.