We propose a flexible Bayesian semiparametric quantile regression model based on Dirichlet process mixtures of generalized asymmetric Laplace distributions for fitting curves with shape restrictions. The generalized asymmetric Laplace distribution exhibits more flexible tail behaviour than the frequently used asymmetric Laplace distribution in Bayesian quantile regression. In addition, nonparametric mixing over the shape and scale parameters with the Dirichlet process mixture extends its flexibility and improves the goodness of fit. By assuming the derivatives of the regression functions to be the squares of the Gaussian processes, our approach ensures that the resulting functions have shape restrictions such as monotonicity, convexity and concavity. The introduction of shape restrictions prevents overfitting and helps obtain smoother and more stable estimates of the quantile curves, especially in the tail quantiles for small and moderate sample sizes. Furthermore, the proposed shape-restricted quantile semiparametric regression model deals with sparse estimation for regression coefficients using the horseshoe+ prior distribution, and it is extended to cases with group-specific curve estimation and censored data. The usefulness of the proposed models is demonstrated using simulated datasets and real applications.

中文翻译：

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广义非对称拉普拉斯分布的狄利克雷过程混合下具有形状限制的灵活贝叶斯分位数曲线拟合

我们提出了一种灵活的贝叶斯半参数分位数回归模型，该模型基于广义不对称拉普拉斯分布的 Dirichlet 过程混合，用于拟合具有形状限制的曲线。广义的非对称拉普拉斯分布比贝叶斯分位数回归中常用的非对称拉普拉斯分布表现出更灵活的尾部行为。此外，形状和尺度参数与 Dirichlet 过程混合物的非参数混合扩展了其灵活性并提高了拟合优度。通过假设回归函数的导数是高斯过程的平方，我们的方法确保结果函数具有形状限制，例如单调性、凸性和凹性。形状限制的引入可防止过度拟合，并有助于获得更平滑、更稳定的分位数曲线估计，尤其是在小样本和中等样本量的尾分位数中。此外，所提出的形状限制分位数半参数回归模型使用马蹄铁+先验分布处理回归系数的稀疏估计，并将其扩展到具有特定组曲线估计和删失数据的情况。使用模拟数据集和实际应用程序证明了所提出模型的有用性。提出的形状限制分位数半参数回归模型使用马蹄铁+先验分布处理回归系数的稀疏估计，并将其扩展到具有特定组曲线估计和删失数据的情况。使用模拟数据集和实际应用程序证明了所提出模型的有用性。提出的形状限制分位数半参数回归模型使用马蹄铁+先验分布处理回归系数的稀疏估计，并将其扩展到具有特定组曲线估计和删失数据的情况。使用模拟数据集和实际应用程序证明了所提出模型的有用性。