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Testing for marginal linear effects in quantile regression

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  • Huixia Judy Wang
  • Ian W. McKeague
  • Min Qian

Abstract

The paper develops a new marginal testing procedure to detect significant predictors that are associated with the conditional quantiles of a scalar response. The idea is to fit the marginal quantile regression on each predictor one at a time, and then to base the test on the t‐statistics that are associated with the most predictive predictors. A resampling method is devised to calibrate this test statistic, which has non‐regular limiting behaviour due to the selection of the most predictive variables. Asymptotic validity of the procedure is established in a general quantile regression setting in which the marginal quantile regression models can be misspecified. Even though a fixed dimension is assumed to derive the asymptotic results, the test proposed is applicable and computationally feasible for large dimensional predictors. The method is more flexible than existing marginal screening test methods based on mean regression and has the added advantage of being robust against outliers in the response. The approach is illustrated by using an application to a human immunodeficiency virus drug resistance data set.

Suggested Citation

  • Huixia Judy Wang & Ian W. McKeague & Min Qian, 2018. "Testing for marginal linear effects in quantile regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 433-452, March.
    • Handle: RePEc:bla:jorssb:v:80:y:2018:i:2:p:433-452
    DOI: 10.1111/rssb.12258
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    Cited by:

    1. Songqiao Tang & Huiyu Wang & Guanao Yan & Lixin Zhang, 2023. "Empirical likelihood based tests for detecting the presence of significant predictors in marginal quantile regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(2), pages 149-179, February.
    2. Mercedes Conde‐Amboage & Ingrid Van Keilegom & Wenceslao González‐Manteiga, 2021. "A new lack‐of‐fit test for quantile regression with censored data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 655-688, June.
    3. Zhan Liu & Xiaoluo Zhao & Yingli Pan, 2023. "Communication-efficient distributed estimation for high-dimensional large-scale linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(4), pages 455-485, May.

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