IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i8p1290-d1634980.html
   My bibliography  Save this article

Estimating Common Mean in Heteroscedastic Variances Model

Author

Listed:
  • Andrew L. Rukhin

    (Department of Mathematics and Statistics, University of Maryland at Baltimore County, Baltimore, MD 21250, USA)

Abstract

Bayes estimators for the unknown mean against a reference, non-informative prior distribution for both the mean and independent variances are derived. I entertain the scenario with two groups of observables with the same unknown mean. The unknown variances of the the first group are not supposed to be equal or to be restricted; the second homeogeneous group of observations all have the same unknown variance. Under the normality condition, these procedures turn out to have a very explicit form of the weighted average with data-dependent weights that admit of a very clear interpretation. The approximate formulas for the variance of the considered estimators and their limiting behavior are also examined. The related “self-dual” orthogonal polynomials and their properties are examined. Recursive formulas for estimators on the basis of these polynomials are developed.

Suggested Citation

  • Andrew L. Rukhin, 2025. "Estimating Common Mean in Heteroscedastic Variances Model," Mathematics, MDPI, vol. 13(8), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1290-:d:1634980
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/8/1290/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/8/1290/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Fernández, Carmen & Steel, Mark F. J., 1999. "Reference priors for the general location-scale modelm," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 377-384, July.
    2. Thomas A. Severini, 2002. "On an exact probability matching property of right-invariant priors," Biometrika, Biometrika Trust, vol. 89(4), pages 952-957, December.
    3. Andrew L. Rukhin, 2017. "Estimation of the common mean from heterogeneous normal observations with unknown variances," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1601-1618, November.
    4. Eric Hand, 2010. "Citizen science: People power," Nature, Nature, vol. 466(7307), pages 685-687, August.
    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. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
    2. Giovanni Brambilla & Francesca Pedrielli, 2020. "Smartphone-Based Participatory Soundscape Mapping for a More Sustainable Acoustic Environment," Sustainability, MDPI, vol. 12(19), pages 1-20, September.
    3. repec:osf:socarx:s6vnw_v1 is not listed on IDEAS
    4. Ebitu, Larmbert & Avery, Helen & Mourad, Khaldoon A. & Enyetu, Joshua, 2021. "Citizen science for sustainable agriculture – A systematic literature review," Land Use Policy, Elsevier, vol. 103(C).
    5. Fernández, Carmen & Steel, Mark F.J., 2000. "Bayesian Regression Analysis With Scale Mixtures Of Normals," Econometric Theory, Cambridge University Press, vol. 16(1), pages 80-101, February.
    6. Andreas Frohlich & Annegret Weng, 2016. "Parameter uncertainty and reserve risk under Solvency II," Papers 1612.03066, arXiv.org, revised Apr 2017.
    7. Ochieng, Hannington Odido & Ojiem, John & Otieno, Joyce, 2019. "Farmer versus Researcher data collection methodologies: Understanding variations and associated trade-offs," AfricArxiv ncw8a, Center for Open Science.
    8. Al Lily, Abdulrahman Essa, 2016. "Crowd-authoring: The art and politics of engaging 101 authors of educational technology," International Journal of Information Management, Elsevier, vol. 36(6), pages 1053-1061.
    9. Brosnan, Tess & Filep, Sebastian & Rock, Jenny, 2015. "Exploring synergies: Hopeful tourism and citizen science," Annals of Tourism Research, Elsevier, vol. 53(C), pages 96-98.
    10. Thomas J. DiCiccio & Todd A. Kuffner & G. Alastair Young, 2017. "A Simple Analysis of the Exact Probability Matching Prior in the Location-Scale Model," The American Statistician, Taylor & Francis Journals, vol. 71(4), pages 302-304, October.
    11. repec:osf:africa:ncw8a_v1 is not listed on IDEAS
    12. Soumya Roy & Biswabrata Pradhan, 2023. "Inference for log‐location‐scale family of distributions under competing risks with progressive type‐I interval censored data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(2), pages 208-232, May.
    13. Benedikt Fecher & Sascha Friesike, 2013. "Open Science: One Term, Five Schools of Thought," RatSWD Working Papers 218, German Data Forum (RatSWD).
    14. Bodnar, Olha & Bodnar, Taras, 2025. "Birge ratio method for modeling dark uncertainty in multivariate meta-analyses and inter-laboratory studies," Journal of Multivariate Analysis, Elsevier, vol. 205(C).
    15. R. Gerrard & A. Tsanakas, 2011. "Failure Probability Under Parameter Uncertainty," Risk Analysis, John Wiley & Sons, vol. 31(5), pages 727-744, May.
    16. Julia Hahn & Miltos Ladikas, 2014. "Responsible Research and Innovation: a Global Perspective," Enterprise and Work Innovation Studies, Universidade Nova de Lisboa, IET/CICS.NOVA-Interdisciplinary Centre on Social Sciences, Faculty of Science and Technology, vol. 10(10), pages 9-27, December.
    17. Jenni Partanen, 2016. "Liquid planning, wiki-design—Learning from the Case Pispala," Environment and Planning B, , vol. 43(6), pages 997-1018, November.
    18. Prpić, John, 2017. "The Contours of Crowd Capability," SocArXiv 9mtzj, Center for Open Science.
    19. Bodnar, Olha & Bodnar, Taras, 2021. "Objective Bayesian meta-analysis based on generalized multivariate random effects model," Working Papers 2021:5, Örebro University, School of Business.
    20. Fröhlich, Andreas & Weng, Annegret, 2018. "Parameter uncertainty and reserve risk under Solvency II," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 130-141.
    21. François-Xavier de Vaujany & Amélie Bohas & Olivier Irrmann, 2019. "Vers une éducation ouverte : Faire, réflexivité et culture pour une éducation-recherche," Working Papers hal-02148965, HAL.
    22. Johannes Halbe & Claudia Pahl-Wostl, 2019. "A Methodological Framework to Initiate and Design Transition Governance Processes," Sustainability, MDPI, vol. 11(3), pages 1-25, February.

    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:gam:jmathe:v:13:y:2025:i:8:p:1290-:d:1634980. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.