IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v60y2019i1d10.1007_s00362-016-0828-x.html
   My bibliography  Save this article

Application of the full Bayesian significance test to model selection under informative sampling

Author

Listed:
  • A. Sikov

    (University of Sao Paulo (IME-USP))

  • J. M. Stern

    (University of Sao Paulo (IME-USP))

Abstract

Adopting likelihood based methods of inference in the case of informative sampling often presents a number of difficulties, particularly, if the parametric form of the model that describes the sample selection mechanism is unknown, and thus requires application of some model selection approach. These difficulties generally arise either due to complexity of the model holding in the sample, or due to identifiability problems. As a remedy we propose alternative approach to model selection and estimation in the case of informative sampling. Our approach is based on weighted estimation equations, where the contribution to the estimation equation from each observation is weighted by the inverse probability of being selected. We show how weighted estimation equations can be incorporated in a Bayesian analysis, and how the full Bayesian significance test can be implemented as a model selection tool. We illustrate the efficiency of the proposed methodology by a simulation study.

Suggested Citation

  • A. Sikov & J. M. Stern, 2019. "Application of the full Bayesian significance test to model selection under informative sampling," Statistical Papers, Springer, vol. 60(1), pages 89-104, February.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:1:d:10.1007_s00362-016-0828-x
    DOI: 10.1007/s00362-016-0828-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0828-x
    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/s00362-016-0828-x?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. Chansoo Kim & Jinhyouk Jung & Younshik Chung, 2011. "Bayesian estimation for the exponentiated Weibull model under Type II progressive censoring," Statistical Papers, Springer, vol. 52(1), pages 53-70, February.
    2. Diego F. de Bernardini & Laura L.R. Rifo, 2011. "Full Bayesian significance test for extremal distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(4), pages 851-863, January.
    3. Jae Kwang Kim & C. J. Skinner, 2013. "Weighting in survey analysis under informative sampling," Biometrika, Biometrika Trust, vol. 100(2), pages 385-398.
    4. Jafar Ahmadi & M. Doostparast, 2006. "Bayesian estimation and prediction for some life distributions based on record values," Statistical Papers, Springer, vol. 47(3), pages 373-392, June.
    5. Tatiana Miazhynskaia & Georg Dorffner, 2006. "A comparison of Bayesian model selection based on MCMC with an application to GARCH-type models," Statistical Papers, Springer, vol. 47(4), pages 525-549, October.
    6. Jean-François Beaumont, 2008. "A new approach to weighting and inference in sample surveys," Biometrika, Biometrika Trust, vol. 95(3), pages 539-553.
    7. Danny Pfeffermann & Fernando Antonio Da Silva Moura & Pedro Luis Do Nascimento Silva, 2006. "Multi-level modelling under informative sampling," Biometrika, Biometrika Trust, vol. 93(4), pages 943-959, December.
    8. Yves Berger, 2004. "A Simple Variance Estimator for Unequal Probability Sampling without Replacement," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(3), pages 305-315.
    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. Michael Sverchkov & Danny Pfeffermann, 2018. "Small area estimation under informative sampling and not missing at random non‐response," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 981-1008, October.
    2. Ray Chambers & Setareh Ranjbar & Nicola Salvati & Barbara Pacini, 2022. "Weighting, informativeness and causal inference, with an application to rainfall enhancement," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1584-1612, October.
    3. Ardia, David & Hoogerheide, Lennart F., 2010. "Efficient Bayesian estimation and combination of GARCH-type models," MPRA Paper 22919, University Library of Munich, Germany.
    4. Nadeem Akhtar & Sajjad Ahmad Khan & Emad A. A. Ismail & Fuad A. Awwad & Akbar Ali Khan & Taza Gul & Haifa Alqahtani, 2024. "Analyzing quantitative performance: Bayesian estimation of 3-component mixture geometric distributions based on Kumaraswamy prior," Statistical Papers, Springer, vol. 65(7), pages 4431-4451, September.
    5. Amini, Morteza & Balakrishnan, N., 2013. "Nonparametric meta-analysis of independent samples of records," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 70-81.
    6. Grigoriy Volovskiy & Udo Kamps, 2020. "Maximum observed likelihood prediction of future record values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 1072-1097, December.
    7. Refah Alotaibi & Mazen Nassar & Hoda Rezk & Ahmed Elshahhat, 2022. "Inferences and Engineering Applications of Alpha Power Weibull Distribution Using Progressive Type-II Censoring," Mathematics, MDPI, vol. 10(16), pages 1-21, August.
    8. Olayan Albalawi & Naresh Chandra Kabdwal & Qazi J. Azhad & Rashi Hora & Basim S. O. Alsaedi, 2022. "Estimation of the Generalized Logarithmic Transformation Exponential Distribution under Progressively Type-II Censored Data with Application to the COVID-19 Mortality Rates," Mathematics, MDPI, vol. 10(7), pages 1-19, March.
    9. D. R. Cox, 2009. "Randomization in the Design of Experiments," International Statistical Review, International Statistical Institute, vol. 77(3), pages 415-429, December.
    10. Xiaolin Luo & Pavel V. Shevchenko, 2012. "Bayesian Model Choice of Grouped t-Copula," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 1097-1119, December.
    11. Matthew R. Williams & Terrance D. Savitsky, 2021. "Uncertainty Estimation for Pseudo‐Bayesian Inference Under Complex Sampling," International Statistical Review, International Statistical Institute, vol. 89(1), pages 72-107, April.
    12. Azeem Ali & Sanku Dey & Haseeb Ur Rehman & Zeeshan Ali, 2019. "On Bayesian reliability estimation of a 1-out-of-k load sharing system model of modified Burr-III distribution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(5), pages 1052-1081, October.
    13. Ahmadi, J. & MirMostafaee, S.M.T.K., 2009. "Prediction intervals for future records and order statistics coming from two parameter exponential distribution," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 977-983, April.
    14. Rashad M. EL-Sagheer, 2018. "Estimation of parameters of Weibull–Gamma distribution based on progressively censored data," Statistical Papers, Springer, vol. 59(2), pages 725-757, June.
    15. Audrone Virbickaite & M. Concepción Ausín & Pedro Galeano, 2015. "Bayesian Inference Methods For Univariate And Multivariate Garch Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 76-96, February.
    16. Christina Empacher & Udo Kamps & Grigoriy Volovskiy, 2023. "Statistical Prediction of Future Sports Records Based on Record Values," Stats, MDPI, vol. 6(1), pages 1-17, January.
    17. He, Zhongfang, 2009. "Forecasting output growth by the yield curve: the role of structural breaks," MPRA Paper 28208, University Library of Munich, Germany.
    18. Fu, Jiayu & Xu, Ancha & Tang, Yincai, 2012. "Objective Bayesian analysis of Pareto distribution under progressive Type-II censoring," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1829-1836.
    19. Jafar Ahmadi & Mohammad Jafari Jozani & Éric Marchand & Ahmad Parsian, 2009. "Prediction of k-records from a general class of distributions under balanced type loss functions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 19-33, June.
    20. Dey, Sanku & Dey, Tanujit & Luckett, Daniel J., 2016. "Statistical inference for the generalized inverted exponential distribution based on upper record values," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 120(C), pages 64-78.

    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:60:y:2019:i:1:d:10.1007_s00362-016-0828-x. 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.