On quantitative trait locus mapping with an interference phenomenon

Charles-Elie Rabier ()

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2014, vol. 23, issue 2, 329 pages

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

Keywords: Quantitative trait locus detection; Likelihood ratio test; Gaussian process; Chi-square process; 62F03; 62F05; 62F12; 62P10 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:testjl:v:23:y:2014:i:2:p:311-329

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DOI: 10.1007/s11749-013-0349-z

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