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On quantitative trait locus mapping with an interference phenomenon

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  • Charles-Elie Rabier

Abstract

We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL (a QTL denotes a gene with quantitative effect on a trait) on the interval [0, T] representing a chromosome. The observation is the trait and the composition of the genome at some locations called “markers”. We focus on the interference phenomenon, i.e. a recombination event inhibits the formation of another recombination event nearby. We give the asymptotic distribution of the LRT process under the null hypothesis that there is no QTL on [0, T] and under local alternatives with a QTL at $$t^{\star}$$ t ⋆ on [0, T]. We show that the LRT process is asymptotically the square of a “linear interpolated and normalized process”. We prove that under the null hypothesis, the distribution of the maximum of the LRT process is the same for a model with or without interference. However, the powers of detection are totally different between the two models. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:23:y:2014:i:2:p:311-329
    DOI: 10.1007/s11749-013-0349-z
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    References listed on IDEAS

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    1. 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 1-35, February.
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    Cited by:

    1. 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.

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