IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v72y2020i1d10.1007_s10463-018-0680-y.html
   My bibliography  Save this article

Inference on a distribution function from ranked set samples

Author

Listed:
  • Lutz Dümbgen

    (University of Bern)

  • Ehsan Zamanzade

    (University of Isfahan)

Abstract

Consider independent observations $$(X_i,R_i)$$(Xi,Ri) with random or fixed ranks $$R_i$$Ri, while conditional on $$R_i$$Ri, the random variable $$X_i$$Xi has the same distribution as the $$R_i$$Ri-th order statistic within a random sample of size k from an unknown distribution function F. Such observation schemes are well known from ranked set sampling and judgment post-stratification. Within a general, not necessarily balanced setting we derive and compare the asymptotic distributions of three different estimators of the distribution function F: a stratified estimator, a nonparametric maximum-likelihood estimator and a moment-based estimator. Our functional central limit theorems generalize and refine previous asymptotic analyses. In addition, we discuss briefly pointwise and simultaneous confidence intervals for the distribution function with guaranteed coverage probability for finite sample sizes. The methods are illustrated with a real data example, and the potential impact of imperfect rankings is investigated in a small simulation experiment.

Suggested Citation

  • Lutz Dümbgen & Ehsan Zamanzade, 2020. "Inference on a distribution function from ranked set samples," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 157-185, February.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:1:d:10.1007_s10463-018-0680-y
    DOI: 10.1007/s10463-018-0680-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-018-0680-y
    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/s10463-018-0680-y?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. Dinesh S. Bhoj, 2001. "Ranked Set Sampling with Unequal Samples," Biometrics, The International Biometric Society, vol. 57(3), pages 957-962, September.
    2. 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.
    3. Ali Dastbaravarde & Nasser Reza Arghami & Majid Sarmad, 2016. "Some theoretical results concerning non parametric estimation by using a judgment poststratification sample," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(8), pages 2181-2203, April.
    4. Steven N. MacEachern & Elizabeth A. Stasny & Douglas A. Wolfe, 2004. "Judgement Post-Stratification with Imprecise Rankings," Biometrics, The International Biometric Society, vol. 60(1), pages 207-215, March.
    5. Jesse Frey & Omer Ozturk, 2011. "Constrained estimation using judgment post-stratification," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(4), pages 769-789, August.
    6. 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.
    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. Mozhgan Alirezaei Dizicheh & Nasrollah Iranpanah & Ehsan Zamanzade, 2021. "Bootstrap Methods for Judgment Post Stratification," Statistical Papers, Springer, vol. 62(5), pages 2453-2471, October.
    2. Soohyun Ahn & Xinlei Wang & Mumu Wang & Johan Lim, 2022. "On continuity correction for RSS-structured cluster randomized designs with binary outcomes," METRON, Springer;Sapienza Università di Roma, vol. 80(3), pages 383-397, December.
    3. Ehsan Zamanzade & M. Mahdizadeh & Hani M. Samawi, 2020. "Efficient estimation of cumulative distribution function using moving extreme ranked set sampling with application to reliability," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(3), pages 485-502, September.
    4. 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.

    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. Mozhgan Alirezaei Dizicheh & Nasrollah Iranpanah & Ehsan Zamanzade, 2021. "Bootstrap Methods for Judgment Post Stratification," Statistical Papers, Springer, vol. 62(5), pages 2453-2471, October.
    2. Omer Ozturk & Olena Kravchuk, 2021. "Judgment Post-stratified Assessment Combining Ranking Information from Multiple Sources, with a Field Phenotyping Example," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 329-348, September.
    3. 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.
    4. Ali Dastbaravarde & Ehsan Zamanzade, 2020. "On estimation of $$P\left( X > Y \right) $$PX>Y based on judgement post stratification," Statistical Papers, Springer, vol. 61(2), pages 767-785, April.
    5. Omer Ozturk, 2019. "Post-stratified Probability-Proportional-to-Size Sampling from Stratified Populations," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 693-718, December.
    6. Xinlei Wang & Johan Lim & Seung-Jean Kim & Kyu Hahn, 2015. "Estimating cell probabilities in contingency tables with constraints on marginals/conditionals by geometric programming with applications," Computational Statistics, Springer, vol. 30(1), pages 107-129, March.
    7. 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.
    8. Jesse Frey & Timothy Feeman, 2013. "Variance estimation using judgment post-stratification," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(3), pages 551-569, June.
    9. Omer Ozturk, 2016. "Estimation of a Finite Population Mean and Total Using Population Ranks of Sample Units," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(1), pages 181-202, March.
    10. Omer Ozturk, 2017. "Statistical inference with empty strata in judgment post stratified samples," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1029-1057, October.
    11. Zamanzade, Ehsan & Wang, Xinlei, 2017. "Estimation of population proportion for judgment post-stratification," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 257-269.
    12. Omer Ozturk, 2019. "Statistical inference using rank-based post-stratified samples in a finite population," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1113-1143, December.
    13. Ozturk, Omer, 2014. "Statistical inference for population quantiles and variance in judgment post-stratified samples," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 188-205.
    14. 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.
    15. Matthews, Michael J. & Wolfe, Douglas A., 2017. "Unified ranked sampling," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 173-178.
    16. Amirhossein Alvandi & Armin Hatefi, 2023. "Analysis of Ordinal Populations from Judgment Post-Stratification," Stats, MDPI, vol. 6(3), pages 1-27, August.
    17. Frey, Jesse & Feeman, Timothy G., 2012. "An improved mean estimator for judgment post-stratification," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 418-426.
    18. 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.
    19. Dinesh S. Bhoj & Girish Chandra, 2024. "Weighted Ranked Set Sampling for Skewed Distributions," Mathematics, MDPI, vol. 12(13), pages 1-11, June.
    20. Amini, Morteza & Balakrishnan, N., 2013. "Nonparametric meta-analysis of independent samples of records," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 70-81.

    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:aistmt:v:72:y:2020:i:1:d:10.1007_s10463-018-0680-y. 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.