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A nonparametric approach for quantile regression.

Mei Ling Huang1, Christine Nguyen2

  • 11Department of Mathematics & Statistics, Brock University, St. Catharines, Ontario, L2S 3A1 Canada.

Journal of Statistical Distributions and Applications
|April 19, 2019
PubMed
Summary
This summary is machine-generated.

This study introduces a direct nonparametric quantile regression method to better estimate conditional quantiles. The new approach offers improved data fitting compared to traditional quantile regression techniques.

Keywords:
Conditional quantileGoodness-of-fitGumbel’s second kind of bivariate exponential distributionNonparametric kernel density estimatorNonparametric regressionWeighted loss function

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Area of Science:

  • Statistics
  • Econometrics

Background:

  • Quantile regression (QR) is widely used for estimating conditional quantiles.
  • Estimating high conditional quantiles is crucial but challenging with traditional QR.
  • Regular QR methods often rely on restrictive linear or non-linear model assumptions.

Purpose of the Study:

  • To propose a novel direct nonparametric quantile regression method.
  • To overcome the limitations of model-specific assumptions in traditional QR.
  • To provide a more flexible approach for estimating conditional quantiles.

Main Methods:

  • A direct nonparametric quantile regression approach is developed.
  • A five-step algorithm is introduced for the estimation process.
  • The proposed method avoids pre-specifying linear or non-linear model structures.

Main Results:

  • Monte Carlo simulations demonstrate the high efficiency of the direct QR estimator.
  • The proposed method shows superior performance compared to the regular QR estimator.
  • Real-world applications confirm the better data fitting of the direct nonparametric quantile regression model.

Conclusions:

  • The direct nonparametric quantile regression method offers a flexible and efficient alternative to traditional QR.
  • This approach provides better model fit for complex datasets.
  • The method is effective for estimating high conditional quantiles in practical scenarios.