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ESTIMATION FOR EXTREME CONDITIONAL QUANTILES OF FUNCTIONAL QUANTILE REGRESSION.

Hanbing Zhu1, Riquan Zhang1, Yehua Li2

  • 1East China Normal University.

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Summary
This summary is machine-generated.

This study introduces a new method for estimating extreme conditional quantiles, improving stability in quantile regression for heavy-tailed data. The novel functional composite quantile regression enhances analysis of response variable tails.

Keywords:
Extrapolationextreme quantileextreme value theoryfunctional principal component analysisfunctional quantile regressionheavy-tailed distribution

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Area of Science:

  • Statistics
  • Econometrics
  • Functional Data Analysis

Background:

  • Quantile regression offers a detailed view of response-covariate relationships, especially at extreme quantiles.
  • Conventional methods struggle with instability in extreme tails due to data sparsity and heavy-tailed distributions.

Purpose of the Study:

  • To develop a novel, stable estimator for extreme conditional quantiles.
  • To address limitations of conventional quantile regression in sparse, heavy-tailed data scenarios.

Main Methods:

  • Functional composite quantile regression incorporating functional principal component analysis.
  • Application of an extrapolation technique from extreme value theory for enhanced tail estimation.
  • Asymptotic normality established under regularity conditions.

Main Results:

  • The proposed estimator demonstrates improved stability and accuracy for extreme conditional quantiles.
  • Monte Carlo simulations confirm superior performance compared to existing estimation methods.
  • Empirical analysis on two real datasets validates the practical utility of the new method.

Conclusions:

  • The novel functional composite quantile regression method provides a robust approach for analyzing extreme quantiles.
  • This technique is particularly valuable for heavy-tailed distributions and sparse data, offering a comprehensive statistical tool.