IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v60y2019i1d10.1007_s00362-016-0835-y.html
   My bibliography  Save this article

Chi-square processes for gene mapping in a population with family structure

Author

Listed:
  • Charles-Elie Rabier

    (MIAT, Université de Toulouse, INRA
    Université Paul Sabatier)

  • Jean-Marc Azaïs

    (Université Paul Sabatier)

  • Jean-Michel Elsen

    (GenPhyse, Université de Toulouse, INRA)

  • Céline Delmas

    (MIAT, Université de Toulouse, INRA)

Abstract

Detecting a quantitative trait locus, so-called QTL (a gene influencing a quantitative trait which is able to be measured), on a given chromosome is a major problem in Genetics. We study a population structured in families and we assume that the QTL location is the same for all the families. We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL on the interval [0, T] representing a chromosome. We give the asymptotic distribution of the LRT process under the null hypothesis that there is no QTL in any families and under local alternative with a QTL at $$t^{\star }\in [0, T]$$ t ⋆ ∈ [ 0 , T ] in at least one family. We show that the LRT is asymptotically the supremum of the sum of the square of independent interpolated Gaussian processes. The number of processes corresponds to the number of families. We propose several new methods to compute critical values for QTL detection. Since all these methods rely on asymptotic results, the validity of the asymptotic assumption is checked using simulated data. Finally we show how to optimize the QTL detecting process.

Suggested Citation

  • Charles-Elie Rabier & Jean-Marc Azaïs & Jean-Michel Elsen & Céline Delmas, 2019. "Chi-square processes for gene mapping in a population with family structure," Statistical Papers, Springer, vol. 60(1), pages 239-271, February.
  • Handle: RePEc:spr:stpapr:v:60:y:2019:i:1:d:10.1007_s00362-016-0835-y
    DOI: 10.1007/s00362-016-0835-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-016-0835-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/s00362-016-0835-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. Charles-Elie Rabier & Alan Genz, 2014. "The Supremum of Chi-Square Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 715-729, September.
    2. Charles-Elie Rabier, 2014. "On quantitative trait locus mapping with an interference phenomenon," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 311-329, June.
    3. Vanessa Didelez & Iris Pigeot & Patricia Walter, 2006. "Modifications of the Bonferroni-Holm procedure for a multi-way ANOVA," Statistical Papers, Springer, vol. 47(2), pages 181-209, March.
    4. Chang Myron N & Wu Rongling & Wu Samuel S & Casella George, 2009. "Score Statistics for Mapping Quantitative Trait Loci," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-37, February.
    5. Estrella, Arturo, 2003. "Critical Values And P Values Of Bessel Process Distributions: Computation And Application To Structural Break Tests," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1128-1143, December.
    6. Byoung Jung & Myoungshic Jhun & Seuck Song, 2007. "A new random permutation test in ANOVA models," Statistical Papers, Springer, vol. 48(1), pages 47-62, 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. Chen, Sanpan & Cui, Guowei & Zhang, Jianhua, 2017. "On testing for structural break of coefficients in factor-augmented regression models," Economics Letters, Elsevier, vol. 161(C), pages 141-145.
    2. Frommlet Florian & Ljubic Ivana & Arnardóttir Helga Björk & Bogdan Malgorzata, 2012. "QTL Mapping Using a Memetic Algorithm with Modifications of BIC as Fitness Function," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-26, May.
    3. Paruolo, Paolo, 2006. "Common trends and cycles in I(2) VAR systems," Journal of Econometrics, Elsevier, vol. 132(1), pages 143-168, May.
    4. Christis Katsouris, 2023. "Predictability Tests Robust against Parameter Instability," Papers 2307.15151, arXiv.org.
    5. Christiansen, Charlotte & Eriksen, Jonas Nygaard & Møller, Stig Vinther, 2014. "Forecasting US recessions: The role of sentiment," Journal of Banking & Finance, Elsevier, vol. 49(C), pages 459-468.
    6. Kim, Dukpa & Perron, Pierre, 2009. "Assessing the relative power of structural break tests using a framework based on the approximate Bahadur slope," Journal of Econometrics, Elsevier, vol. 149(1), pages 26-51, April.
    7. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2010. "Regime specific predictability in predictive regressions," Discussion Paper Series In Economics And Econometrics 0916, Economics Division, School of Social Sciences, University of Southampton.
    8. Matthew Davis & Fernando V. Ferreira, 2017. "Housing Disease and Public School Finances," NBER Working Papers 24140, National Bureau of Economic Research, Inc.
    9. Tom Campbell & Nathaniel T. Wilcox, 2020. "Younger Federal District Court Judges Favor Presidential Power," Journal of Law and Economics, University of Chicago Press, vol. 63(1), pages 181-202.
    10. Charles-Elie Rabier, 2014. "On quantitative trait locus mapping with an interference phenomenon," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 311-329, June.
    11. Castro, Carlos & Ferrari, Stijn, 2014. "Measuring and testing for the systemically important financial institutions," Journal of Empirical Finance, Elsevier, vol. 25(C), pages 1-14.
    12. Sandip Sinharay, 2016. "Person Fit Analysis in Computerized Adaptive Testing Using Tests for a Change Point," Journal of Educational and Behavioral Statistics, , vol. 41(5), pages 521-549, October.
    13. Davis, Matthew & Ferreira, Fernando, 2022. "Housing disease and public school finances," Economics of Education Review, Elsevier, vol. 88(C).
    14. Hidalgo, Javier & Schafgans, Marcia, 2017. "Inference and testing breaks in large dynamic panels with strong cross sectional dependence," Journal of Econometrics, Elsevier, vol. 196(2), pages 259-274.
    15. Jesús Gonzalo & Jean-Yves Pitarakis, 2011. "Regime-Specific Predictability in Predictive Regressions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(2), pages 229-241, June.
    16. Piterbarg, Vladimir I. & Rodionov, Igor V., 2020. "High excursions of Bessel and related random processes," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4859-4872.
    17. Heikki Kauppi, 2008. "Yield-Curve Based Probit Models for Forecasting U.S. Recessions: Stability and Dynamics," Discussion Papers 31, Aboa Centre for Economics.
    18. Omtzigt, Pieter & Paruolo, Paolo, 2005. "Impact factors," Journal of Econometrics, Elsevier, vol. 128(1), pages 31-68, September.
    19. Ng, Eric C.Y., 2012. "Forecasting US recessions with various risk factors and dynamic probit models," Journal of Macroeconomics, Elsevier, vol. 34(1), pages 112-125.
    20. A. Batsidis & N. Martín & L. Pardo & K. Zografos, 2016. "ϕ-Divergence Based Procedure for Parametric Change-Point Problems," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 21-35, March.

    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_s00362-016-0835-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.