Over the last decades, the challenges in applied regression have been changing considerably, and full probabilistic modeling rather than predicting just means is crucial in many applications. Motivated by two applications where the response variable is observed on the unit-interval and inflated at zero or one, we propose a parametric quantile regression considering the unit-Weibull distribution. In particular, we are interested in quantifying the influence of covariates on the quantiles of the response variable. The maximum likelihood method is used for parameters estimation. Monte Carlo simulations reveal that the maximum likelihood estimators are nearly unbiased and consistent. Also, we define a residual analysis to assess the goodness of fit.

中文翻译：

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一种用于建模零或一膨胀双界数据的参数分位数回归方法

在过去的几十年里，应用回归的挑战发生了很大的变化，在许多应用中，完整的概率建模而不是仅预测均值至关重要。受两个应用的启发，其中响应变量在单位区间上观察到并在零或一处膨胀，我们提出了考虑单位威布尔分布的参数分位数回归。特别是，我们对量化协变量对响应变量分位数的影响很感兴趣。最大似然法用于参数估计。Monte Carlo 模拟显示最大似然估计量几乎无偏且一致。此外，我们定义了残差分析来评估拟合优度。