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Testing for Marginal Linear Effects in Quantile Regression.

Huixia Judy Wang1, Ian W McKeague2, Min Qian3

  • 1Associate Professor, Department of Statistics, George Washington University, Washington, District of Columbia 20052, USA.

Journal of the Royal Statistical Society. Series B, Statistical Methodology
|March 27, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces a new statistical test to identify important predictors for conditional quantiles. The method is robust, handles large datasets, and is effective even when models are misspecified.

Keywords:
Bootstrap calibrationinferencemarginal regressionnon-standard asymptoticsquantile regression

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • Identifying significant predictors is crucial for understanding complex relationships in data.
  • Existing methods often rely on mean regression and can be sensitive to outliers.

Purpose of the Study:

  • To develop a novel marginal testing procedure for detecting significant predictors of conditional quantiles.
  • To provide a flexible and robust method applicable to high-dimensional data.

Main Methods:

  • Fitting marginal quantile regression models for each predictor individually.
  • Utilizing t-statistics from the most predictive variables.
  • Employing a resampling method to calibrate the test statistic due to variable selection.

Main Results:

  • The procedure is asymptotically valid, even with misspecified marginal models.
  • It is computationally feasible for large-dimensional predictors.
  • Demonstrated robustness against outliers in the response variable.

Conclusions:

  • The proposed marginal testing procedure offers a flexible alternative to existing methods.
  • It is suitable for identifying key predictors in quantile regression, particularly in high-dimensional settings.
  • The method shows practical utility, as evidenced by its application to HIV drug resistance data.