An asymptotic test for Quantitative Trait Locus detection in presence of missing genotypes

Charles-Elie Rabier

Annales de la faculté des sciences de Toulouse Mathématiques (2014)

  • Volume: 23, Issue: 4, page 755-778
  • ISSN: 0240-2963

Abstract

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We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait) on the interval [ 0 , T ] representing a chromosome. The originality is in the fact that some genotypes are missing. We give the asymptotic distribution of this LRT process under the null hypothesis that there is no QTL on [ 0 , T ] and under local alternatives with a QTL at t ☆ on [ 0 , T ] . We show that the LRT process is asymptotically the square of a “non-linear interpolated and normalized Gaussian process”. We have an easy formula in order to compute the supremum of the square of this interpolated process. We prove that the threshold is exactly the same as in the classical situation without missing genotypes.

How to cite

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Rabier, Charles-Elie. "An asymptotic test for Quantitative Trait Locus detection in presence of missing genotypes." Annales de la faculté des sciences de Toulouse Mathématiques 23.4 (2014): 755-778. <http://eudml.org/doc/275282>.

@article{Rabier2014,
abstract = {We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait) on the interval $[0,T]$ representing a chromosome. The originality is in the fact that some genotypes are missing. We give the asymptotic distribution of this LRT process under the null hypothesis that there is no QTL on $[0,T]$ and under local alternatives with a QTL at $t^\{\star \}$ on $[0,T]$. We show that the LRT process is asymptotically the square of a “non-linear interpolated and normalized Gaussian process”. We have an easy formula in order to compute the supremum of the square of this interpolated process. We prove that the threshold is exactly the same as in the classical situation without missing genotypes.},
author = {Rabier, Charles-Elie},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
number = {4},
pages = {755-778},
publisher = {Université Paul Sabatier, Toulouse},
title = {An asymptotic test for Quantitative Trait Locus detection in presence of missing genotypes},
url = {http://eudml.org/doc/275282},
volume = {23},
year = {2014},
}

TY - JOUR
AU - Rabier, Charles-Elie
TI - An asymptotic test for Quantitative Trait Locus detection in presence of missing genotypes
JO - Annales de la faculté des sciences de Toulouse Mathématiques
PY - 2014
PB - Université Paul Sabatier, Toulouse
VL - 23
IS - 4
SP - 755
EP - 778
AB - We consider the likelihood ratio test (LRT) process related to the test of the absence of QTL (a QTL denotes a quantitative trait locus, i.e. a gene with quantitative effect on a trait) on the interval $[0,T]$ representing a chromosome. The originality is in the fact that some genotypes are missing. We give the asymptotic distribution of this LRT process under the null hypothesis that there is no QTL on $[0,T]$ and under local alternatives with a QTL at $t^{\star }$ on $[0,T]$. We show that the LRT process is asymptotically the square of a “non-linear interpolated and normalized Gaussian process”. We have an easy formula in order to compute the supremum of the square of this interpolated process. We prove that the threshold is exactly the same as in the classical situation without missing genotypes.
LA - eng
UR - http://eudml.org/doc/275282
ER -

References

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