Flexible Bayesian quantile curve fitting with shape restrictions under the Dirichlet process mixture of the generalized asymmetric Laplace distribution
Flexible Bayesian quantile curve fitting with shape restrictions under the Dirichlet process mixture of the generalized asymmetric Laplace distribution
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DOI：
10.1002/cjs.11582
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发表时间：
2020-11-04
影响因子：
0.6
通讯作者：
Choi, Taeryon
中科院分区：
文献类型：
--
作者：
Kobayashi, Genya;Roh, Taeyoung;Choi, Taeryon
提出了一种基于广义非对称拉普拉斯分布Dirichlet过程混合的弹性贝叶斯半参数分位数回归模型，用于拟合具有形状限制的曲线.广义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具有更灵活的尾部行为。此外，非参数混合的形状和尺度参数的Dirichlet过程混合扩展其灵活性，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，我们的方法确保了得到的函数具有形状限制，如单调性，凸性和凸性。形状限制的引入防止了过度拟合，并有助于获得更平滑和更稳定的分位数曲线估计，特别是在小样本和中等样本量的尾部分位数中。此外，所提出的形状限制分位数半参数回归模型处理稀疏估计的回归系数使用马蹄+先验分布，它被扩展到特定组的曲线估计和删失数据的情况下。使用模拟数据集和真实的应用程序证明了所提出的模型的有用性。
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.