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The unit generalized half-normal quantile regression model: formulation, estimation, diagnostics, and numerical

Josmar Mazucheli1, Mustafa Ç Korkmaz2, André F B Menezes3

  • 1Department of Statistics, Universidade Estadual de Maringá, Maringá, Brazil.

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Summary
This summary is machine-generated.

This study introduces a novel regression model for data on the unit interval, offering an alternative to existing quantile regression methods. The new model provides insights into explanatory variable effects on conditional quantiles.

Keywords:
Kumaraswamy distributionLikelihood methodsMonte Carlo simulationR softwareResidual analysisUnit generalized half-normal distribution.

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Area of Science:

  • Statistics
  • Econometrics
  • Biostatistics

Background:

  • Regression models are essential for analyzing relationships between variables.
  • Existing models may not adequately capture the behavior of response variables constrained to the unit interval (0, 1).
  • Quantile regression offers a more comprehensive understanding of variable effects beyond the mean.

Purpose of the Study:

  • To propose and derive a new regression model for response variables defined on the open unit interval.
  • To offer an alternative to the Kumaraswamy quantile regression model.
  • To interpret the location parameter of the reparameterized unit generalized half-normal distribution as a quantile.

Main Methods:

  • Reparameterization of the unit generalized half-normal distribution.
  • Development of a new regression framework for unit interval data.
  • Comparative analysis with the Kumaraswamy quantile regression model using simulated and real-world data.

Main Results:

  • The proposed regression model effectively fits data on the unit interval.
  • The location parameter of the reparameterized distribution is interpretable as a quantile.
  • The new model demonstrates competitive or superior performance compared to the Kumaraswamy model in real applications.

Conclusions:

  • The proposed unit interval regression model is a valuable addition to statistical modeling tools.
  • It provides a flexible and interpretable approach for analyzing data bounded between 0 and 1.
  • The model's utility is confirmed through simulation studies and practical data analysis.