IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v21y2019i4d10.1007_s11009-018-9671-y.html
   My bibliography  Save this article

Constructions of New Classes of One- and Two-Sample Nonparametric Location Tests

Author

Listed:
  • Bhargab Chattopadhyay

    (Indian Institute of Information Technology Vadodara)

  • Nitis Mukhopadhyay

    (University of Connecticut)

Abstract

In this paper, we examine the role of nonparametric test statistics with constructions analogous to those introduced in Mukhopadhyay and Chattopadhyay (Stat Pap 54:827–837 2013) and Mukhopadhyay and Chattopadhyay (Sri Lankan J Appl Stat 15:71–80 2014) in the context of one-sample and two-sample location problems. In the case of a one-sample location problem, we focus on the customary sign test and its appropriate modifications. In the case of a two-sample location problem, we focus on Mann-Whitney test when the population distribution F remains unknown. Using large sample approximations, we propose new versions of tests and compare their performances with those of the customary sign and Mann-Whitney tests. We do so on the basis of asymptotic power, asymptotic efficiency, and robustness. Our present treatment substantially broadens the coverage found in Walsh (Ann Math Stat 17:360–361 1946, Ann Math Stat 20:64–81 1949) and Ylvisaker (J Am Stat Assoc 72:551–556 1977. In summary, we have come up with (i) a test that is more efficient than a sign test, and (ii) a limited optimality of Mann-Whitney test within our class of newly constructed tests.

Suggested Citation

  • Bhargab Chattopadhyay & Nitis Mukhopadhyay, 2019. "Constructions of New Classes of One- and Two-Sample Nonparametric Location Tests," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1229-1249, December.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:4:d:10.1007_s11009-018-9671-y
    DOI: 10.1007/s11009-018-9671-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-018-9671-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/s11009-018-9671-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. N. Mukhopadhyay & T. Solanky, 1997. "Estimation after sequential selection and ranking," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 95-106, January.
    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. Nitis Mukhopadhyay & Tumulesh K. S. Solanky, 2012. "On Two-Stage Comparisons with a Control Under Heteroscedastic Normal Distributions," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 501-522, September.
    2. Bandyopadhyay, Uttam & Sarkar, Suman & Biswas, Atanu, 2022. "Sequential confidence interval for comparing two Bernoulli distributions in a non-conventional set-up," Statistics & Probability Letters, Elsevier, vol. 181(C).
    3. Kazuyoshi Yata & Makoto Aoshima, 2012. "Inference on High-Dimensional Mean Vectors with Fewer Observations Than the Dimension," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 459-476, September.
    4. Nitis Mukhopadhyay & Srawan Kumar Bishnoi, 2021. "An Unusual Application of Cramér-Rao Inequality to Prove the Attainable Lower Bound for a Ratio of Complicated Gamma Functions," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1507-1517, December.
    5. Sudeep R. Bapat, 2023. "A novel sequential approach to estimate functions of parameters of two gamma populations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(6), pages 627-641, August.
    6. Nitis Mukhopadhyay & Soumik Banerjee, 2023. "A General Theory of Three-Stage Estimation Strategy with Second-Order Asymptotics and Its Applications," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 401-440, February.
    7. Hwang, Leng-Cheng, 2020. "A robust two-stage procedure for the Poisson process under the linear exponential loss function," Statistics & Probability Letters, Elsevier, vol. 163(C).
    8. Christopher S. Withers & Saralees Nadarajah, 2022. "Cornish-Fisher Expansions for Functionals of the Weighted Partial Sum Empirical Distribution," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1791-1804, September.
    9. Nitis Mukhopadhyay, 2010. "On a Sharper Lower Bound for a Percentile of a Student’s t Distribution with an Application," Methodology and Computing in Applied Probability, Springer, vol. 12(4), pages 609-622, December.
    10. Makoto Aoshima & Kazuyoshi Yata, 2015. "Asymptotic Normality for Inference on Multisample, High-Dimensional Mean Vectors Under Mild Conditions," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 419-439, June.
    11. Ajit Chaturvedi & Sudeep R. Bapat & Neeraj Joshi, 2020. "Purely Sequential and k-Stage Procedures for Estimating the Mean of an Inverse Gaussian Distribution," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1193-1219, September.
    12. S. Zacks, 2007. "Review of Some Functionals of Compound Poisson Processes and Related Stopping Times," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 343-356, June.

    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:metcap:v:21:y:2019:i:4:d:10.1007_s11009-018-9671-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.