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Distance-Based Analysis with Quantile Regression Models

Author

Listed:
  • Shaoyu Li

    (University of North Carolina at Charlotte)

  • Yanqing Sun

    (University of North Carolina at Charlotte)

  • Liyang Diao

    (Seres Therapeutics)

  • Xue Wang

    (Mayo Clinic)

Abstract

Non-standard structured, multivariate data are emerging in many research areas, including genetics and genomics, ecology, and social science. Suitably defined pairwise distance measures are commonly used in distance-based analysis to study the association between the variables. In this work, we consider a linear quantile regression model for pairwise distances. We investigate the large sample properties of an estimator of the unknown coefficients and propose statistical inference procedures correspondingly. Extensive simulations provide evidence of satisfactory finite sample properties of the proposed method. Finally, we applied the method to a microbiome association study to illustrate its utility.

Suggested Citation

  • Shaoyu Li & Yanqing Sun & Liyang Diao & Xue Wang, 2021. "Distance-Based Analysis with Quantile Regression Models," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(2), pages 291-312, July.
    • Handle: RePEc:spr:stabio:v:13:y:2021:i:2:d:10.1007_s12561-021-09306-6
    DOI: 10.1007/s12561-021-09306-6
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    References listed on IDEAS

    as
    1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    2. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    3. Roger Koenker & Kevin F. Hallock, 2001. "Quantile Regression," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 143-156, Fall.
    4. Honore, Bo E. & Powell, James L., 1994. "Pairwise difference estimators of censored and truncated regression models," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 241-278.
    Full references (including those not matched with items on IDEAS)

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