IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v135y2019icp35-55.html
   My bibliography  Save this article

Estimation of mean residual life based on ranked set sampling

Author

Listed:
  • Zamanzade, Elham
  • Parvardeh, Afshin
  • Asadi, Majid

Abstract

The mean residual life (MRL) of a nonnegative random variable X plays an important role in various disciplines such as reliability, survival analysis, and extreme value theory. This paper deals with the problem of estimating the MRL in ranked set sampling (RSS) design. An RSS-based estimator for MRL is proposed and its properties are investigated. For finite sample sizes, a Monte Carlo simulation study is carried out to show that the resulting estimator is more efficient than its counterpart in simple random sampling (SRS) design. It is proved that the proposed estimator asymptotically follows a Gaussian process and its asymptotic variance is no larger than its counterpart in the SRS design, regardless of the quality of ranking. Different methods of constructing a confidence interval for MRL in the RSS and SRS designs are then discussed. It is observed that while both the RSS and SRS-based confidence intervals do not control the nominal confidence level equally well, the RSS-based confidence intervals have generally shorter lengths than those in the SRS scheme. Finally, a potential application in the context of medical studies is presented for illustration purpose.

Suggested Citation

  • Zamanzade, Elham & Parvardeh, Afshin & Asadi, Majid, 2019. "Estimation of mean residual life based on ranked set sampling," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 35-55.
    • Handle: RePEc:eee:csdana:v:135:y:2019:i:c:p:35-55
    DOI: 10.1016/j.csda.2019.01.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947319300064
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2019.01.005?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. Terrence Hui & Reza Modarres & Gang Zheng, 2009. "Pseudo maximum likelihood estimates using ranked set sampling with applications to estimating correlation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 365-380, August.
    2. Kwun Chuen Gary Chan & Ying Qing Chen & Chong-Zhi Di, 2012. "Proportional mean residual life model for right-censored length-biased data," Biometrika, Biometrika Trust, vol. 99(4), pages 995-1000.
    3. Y. Q. Chen & N. P. Jewell & X. Lei & S. C. Cheng, 2005. "Semiparametric Estimation of Proportional Mean Residual Life Model in Presence of Censoring," Biometrics, The International Biometric Society, vol. 61(1), pages 170-178, March.
    4. Frey, Jesse & Ozturk, Omer & Deshpande, Jayant V., 2007. "Nonparametric Tests for Perfect Judgment Rankings," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 708-717, June.
    5. Modarres, Reza & Hui, Terrence P. & Zheng, Gang, 2006. "Resampling methods for ranked set samples," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1039-1050, November.
    6. Omer Ozturk & N. Balakrishnan, 2009. "Exact two-sample nonparametric test for quantile difference between two populations based on ranked set samples," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 235-249, March.
    7. N. Balakrishnan & T. Li, 2006. "Confidence Intervals for Quantiles and Tolerance Intervals Based on Ordered Ranked Set Samples," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(4), pages 757-777, December.
    8. Ehsan Zamanzade & Xinlei Wang, 2018. "Proportion estimation in ranked set sampling in the presence of tie information," Computational Statistics, Springer, vol. 33(3), pages 1349-1366, September.
    9. Ahn, Soohyun & Wang, Xinlei & Lim, Johan, 2017. "On unbalanced group sizes in cluster randomized designs using balanced ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 210-217.
    10. Steven N. MacEachern & Ömer Öztürk & Douglas A. Wolfe & Gregory V. Stark, 2002. "A new ranked set sample estimator of variance," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 177-188, May.
    11. M. Mahdizadeh & Ehsan Zamanzade, 2018. "A new reliability measure in ranked set sampling," Statistical Papers, Springer, vol. 59(3), pages 861-891, September.
    12. Frey, Jesse & Wang, Le, 2013. "Most powerful rank tests for perfect rankings," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 157-168.
    13. Zamanzade, Ehsan & Arghami, Nasser Reza & Vock, Michael, 2012. "Permutation-based tests of perfect ranking," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2213-2220.
    14. Jesse Frey, 2012. "Constrained nonparametric estimation of the mean and the CDF using ranked-set sampling with a covariate," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 439-456, April.
    15. Ghosh, Souvik & Resnick, Sidney, 2010. "A discussion on mean excess plots," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1492-1517, August.
    16. Ehsan Zamanzade & Nasser Reza Arghami & Michael Vock, 2014. "A Parametric Test of Perfect Ranking in Balanced Ranked Set Sampling," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(21), pages 4589-4611, November.
    17. Xinlei Wang & Johan Lim & Lynne Stokes, 2016. "Using Ranked Set Sampling With Cluster Randomized Designs for Improved Inference on Treatment Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1576-1590, 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. Elham Zamanzade & Majid Asadi & Afshin Parvardeh & Ehsan Zamanzade, 2023. "A ranked-based estimator of the mean past lifetime with an application," Statistical Papers, Springer, vol. 64(1), pages 161-177, February.

    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. Ehsan Zamanzade & Michael Vock, 2018. "Some nonparametric tests of perfect judgment ranking for judgment post stratification," Statistical Papers, Springer, vol. 59(3), pages 1085-1100, September.
    2. Zamanzade, Ehsan & Vock, Michael, 2015. "Variance estimation in ranked set sampling using a concomitant variable," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 1-5.
    3. Elham Zamanzade & Majid Asadi & Afshin Parvardeh & Ehsan Zamanzade, 2023. "A ranked-based estimator of the mean past lifetime with an application," Statistical Papers, Springer, vol. 64(1), pages 161-177, February.
    4. Xinlei Wang & Ke Wang & Johan Lim, 2012. "Isotonized CDF Estimation from Judgment Poststratification Data with Empty Strata," Biometrics, The International Biometric Society, vol. 68(1), pages 194-202, March.
    5. Cesar Augusto Taconeli & Suely Ruiz Giolo, 2020. "Maximum likelihood estimation based on ranked set sampling designs for two extensions of the Lindley distribution with uncensored and right-censored data," Computational Statistics, Springer, vol. 35(4), pages 1827-1851, December.
    6. Zamanzade, Ehsan & Wang, Xinlei, 2017. "Estimation of population proportion for judgment post-stratification," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 257-269.
    7. Saeid Amiri & Reza Modarres & Silvelyn Zwanzig, 2017. "Tests of perfect judgment ranking using pseudo-samples," Computational Statistics, Springer, vol. 32(4), pages 1309-1322, December.
    8. Nikolay I. Nikolov & Eugenia Stoimenova, 2020. "Mallows’ models for imperfect ranking in ranked set sampling," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 459-484, September.
    9. Hamid Rahmani & Mostafa Razmkhah, 2017. "Perfect ranking test in moving extreme ranked set sampling," Statistical Papers, Springer, vol. 58(3), pages 855-875, September.
    10. Frey, Jesse & Wang, Le, 2013. "Most powerful rank tests for perfect rankings," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 157-168.
    11. Yang, Guangren & Zhou, Yong, 2014. "Semiparametric varying-coefficient study of mean residual life models," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 226-238.
    12. M. Mahdizadeh & Ehsan Zamanzade, 2018. "Interval estimation of $$P(X," Computational Statistics, Springer, vol. 33(3), pages 1325-1348, September.
    13. Zamanzade, Ehsan & Mahdizadeh, M., 2017. "A more efficient proportion estimator in ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 28-33.
    14. Ehsan Zamanzade & Xinlei Wang, 2018. "Proportion estimation in ranked set sampling in the presence of tie information," Computational Statistics, Springer, vol. 33(3), pages 1349-1366, September.
    15. Zeinab Akbari Ghamsari & Ehsan Zamanzade & Majid Asadi, 2024. "Using nomination sampling in estimating the area under the ROC curve," Computational Statistics, Springer, vol. 39(5), pages 2721-2742, July.
    16. Omer Ozturk & N. Balakrishnan, 2009. "An Exact Control-Versus-Treatment Comparison Test Based on Ranked Set Samples," Biometrics, The International Biometric Society, vol. 65(4), pages 1213-1222, December.
    17. M. Mahdizadeh & Ehsan Zamanzade, 2022. "New insights on goodness-of-fit tests for ranked set samples," Statistical Papers, Springer, vol. 63(6), pages 1777-1799, December.
    18. Chi Hyun Lee & Jing Ning & Yu Shen, 2019. "Model diagnostics for the proportional hazards model with length-biased data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 79-96, January.
    19. Kyu Hyun Kim & Daniel J. Caplan & Sangwook Kang, 2023. "Smoothed quantile regression for censored residual life," Computational Statistics, Springer, vol. 38(2), pages 1001-1022, June.
    20. Peter Grundke & Kamil Pliszka, 2018. "A macroeconomic reverse stress test," Review of Quantitative Finance and Accounting, Springer, vol. 50(4), pages 1093-1130, 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:eee:csdana:v:135:y:2019:i:c:p:35-55. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.