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Quantile regression via vector generalized additive models.

Thomas W Yee1

  • 1Department of Statistics, University of Auckland, Private Bag 92019, Auckland 1001, New Zealand. statwy@stat.nus.edu.sg, t.yee@auckland.ac.nz

Statistics in Medicine
|July 6, 2004
PubMed
Summary

The LMS method enhances quantile regression using Box-Cox transformations for standard normality. A new Yeo-Johnson transformation method is introduced, allowing for non-positive responses and efficient software implementation.

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Area of Science:

  • Statistics
  • Econometrics

Background:

  • The Least Mean Squares (LMS) method is a popular quantile regression technique.
  • It utilizes a penalized likelihood framework and cubic smoothing splines for flexibility.
  • The standard LMS method employs a Box-Cox transformation for positive responses.

Purpose of the Study:

  • Present LMS quantile regression within the Vector Generalized Additive Models (VGAMs) framework.
  • Introduce a novel LMS method using the Yeo-Johnson transformation for broader applicability.
  • Describe a software implementation of LMS methods in the S language.

Main Methods:

  • Vector Generalized Additive Models (VGAMs) framework for LMS quantile regression.
  • Development of a new LMS method employing the Yeo-Johnson transformation.

Related Experiment Videos

  • Efficient numerical integration scheme for estimating the LMS-Yeo-Johnson method.

    • Main Results:

    • Integration of LMS quantile regression into the unifying VGAMs framework.
    • Introduction of the LMS-Yeo-Johnson method, accommodating non-positive responses.
    • Successful software implementation and illustration using New Zealand working population data.

    Conclusions:

    • The VGAMs framework provides a unified approach to LMS quantile regression.
    • The LMS-Yeo-Johnson method expands the applicability of LMS quantile regression.
    • The developed software facilitates the application of these advanced statistical methods.