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Hypothesis testing for quantitative trait locus effects in both location and scale in genetic backcross studies

Author

Listed:
  • Guanfu Liu
  • Pengfei Li
  • Yukun Liu
  • Xiaolong Pu

Abstract

Testing the existence of a quantitative trait locus (QTL) effect is an important task in QTL mapping studies. Most studies concentrate on the case where the phenotype distributions of different QTL groups follow normal distributions with the same unknown variance. In this paper we make a more general assumption that the phenotype distributions come from a location‐scale distribution family. We derive the limiting distribution of the likelihood ratio test (LRT) for the existence of the QTL effect in both location and scale in genetic backcross studies. We further identify an explicit representation for this limiting distribution. As a complement, we study the limiting distribution of the LRT and its explicit representation for the existence of the QTL effect in the location only. The asymptotic properties of the LRTs under a local alternative are also investigated. Simulation studies are used to evaluate the asymptotic results, and a real‐data example is included for illustration.

Suggested Citation

  • Guanfu Liu & Pengfei Li & Yukun Liu & Xiaolong Pu, 2020. "Hypothesis testing for quantitative trait locus effects in both location and scale in genetic backcross studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1064-1089, December.
    • Handle: RePEc:bla:scjsta:v:47:y:2020:i:4:p:1064-1089
    DOI: 10.1111/sjos.12442
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    References listed on IDEAS

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    1. Zhang, Hong & Chen, Hanfeng & Li, Zhaohai, 2008. "An explicit representation of the limit of the LRT for interval mapping of quantitative trait loci," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 207-213, February.
    2. Gu, Jiaying & Koenker, Roger & Volgushev, Stanislav, 2018. "Testing For Homogeneity In Mixture Models," Econometric Theory, Cambridge University Press, vol. 34(4), pages 850-895, August.
    3. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, August.
    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.
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    1. Pengcheng Ren & Guanfu Liu & Xiaolong Pu & Xingyu Yan, 2025. "A Note for Likelihood Ratio Methods for Testing the Homogeneity of a Three-Sample Problem with a Mixture Structure," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 87(1), pages 114-133, February.

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