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A parametric quantile regression approach for modelling zero-or-one inflated double bounded data.

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Summary
This summary is machine-generated.

This study introduces a new parametric quantile regression model using the unit-Weibull distribution for data on the unit-interval. The method accurately quantifies covariate influence on response variable quantiles.

Keywords:
parametric quantile regressionproportionsunit-Weibull distributionzero-or-one inflated models

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Area of Science:

  • Statistics
  • Econometrics

Background:

  • Applied regression analysis increasingly requires full probabilistic modeling beyond mean prediction.
  • Unit-interval data, especially with zero or one inflation, presents unique modeling challenges.

Purpose of the Study:

  • To propose a parametric quantile regression model for unit-interval data.
  • To quantify the influence of covariates on the quantiles of a response variable.
  • To introduce a robust method for analyzing data bounded between 0 and 1.

Main Methods:

  • Development of a parametric quantile regression model utilizing the unit-Weibull distribution.
  • Parameter estimation via the maximum likelihood method.
  • Definition of a residual analysis for assessing model fit.

Main Results:

  • Maximum likelihood estimators demonstrated to be nearly unbiased and consistent through Monte Carlo simulations.
  • The proposed model effectively captures the behavior of unit-interval data.
  • The residual analysis provides a reliable tool for evaluating model performance.

Conclusions:

  • The unit-Weibull quantile regression model offers a powerful tool for analyzing bounded data.
  • The method is suitable for applications requiring detailed understanding of covariate effects across the entire distribution.
  • The statistical properties of the estimators support the model's reliability.