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Quantitative analysis is a technique for measuring the amount of specific constituents in a sample. When the sample's composition is unknown, qualitative analysis is performed first to identify its components, which ensures that the correct substances are measured during the quantitative phase.
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Inference in Functional Linear Quantile Regression.

Meng Li1, Kehui Wang2, Arnab Maity3

  • 1Department of Statistics, Rice University, Houston, TX.

Journal of Multivariate Analysis
|April 4, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces a new statistical method for functional quantile regression, enabling analysis of how functional data influences response quantiles. The developed testing procedure is effective even with sparse and noisy data.

Keywords:
Composite quantile regressionFunctional principal component analysisFunctional quantile regressionMeasurement errorPrimary 62G08Secondary 62H15Wald test

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Area of Science:

  • Statistics
  • Econometrics
  • Functional Data Analysis

Background:

  • Functional quantile regression extends traditional methods to handle functional covariates.
  • Existing methods may lack robust inference for complex functional relationships.

Purpose of the Study:

  • To develop statistical inference for functional quantile regression with scalar response and functional covariate.
  • To test if the regression parameter function is constant across quantile levels.

Main Methods:

  • A functional linear quantile regression model is proposed.
  • Parameter estimation combines functional principal component analysis and quantile regression.
  • An adjusted Wald testing procedure is developed with derived chi-square asymptotic null distribution.

Main Results:

  • The proposed testing procedure demonstrates effectiveness in simulations.
  • The method performs well with sparse and noisy functional covariates.
  • The approach is validated using a capital bike share data application.

Conclusions:

  • The developed method provides a robust framework for statistical inference in functional quantile regression.
  • The adjusted Wald test offers a reliable tool for hypothesis testing in this context.
  • The approach is computationally accessible, with R code available online.