基于径向基的自适应惩罚样条回归模型

传统惩罚样条回归模型中惩罚项的设置未考虑数据的空间异质性,因而对复杂数据的拟合缺乏自适应性.文章通过对径向基函数的几何意义分析,以节点两侧相邻区域内数据点的纵向极差为基础,构造局部惩罚权重向量并加入到约束回归模型的惩罚项中,构造了基于径向基的自适应惩罚样条回归模型.新模型在观测数据波动较大的区域,给予拟合曲线较小的惩罚,而在观测数据波动较小的区域,给予拟合曲线较大的惩罚,从而使拟合曲线能自适应地反映观测数据的局部变化特征.模拟和应用结果显示新模型的拟合效果显著优于传统的惩罚样条回归模型.     

Quantile regression with an epsilon-insensitive loss in a reproducing kernel Hilbert space

This paper proposes a method to estimate the conditional quantile function using an epsilon-insensitive loss in a reproducing kernel Hilbert space. When choosing a smoothing parameter in nonparametric frameworks, it is necessary to evaluate the complexity of the model. In this regard, we provide a simple formula for computing an effective number of parameters when implementing an epsilon-insensitive loss. We also investigate the effects of the epsilon-insensitive loss.     

删失分位数回归模型基于扩展兴趣信息准则的平均估计

本文结合分位数回归技术,基于删失回归模型,把Claeskens和Hjort的传统兴趣信息准侧(focused information criterion,FIC)扩展到兴趣向量的情形,提出扩展的兴趣信息准则(extended focused information criterion,E-FIC),有效解决了同时针对多个兴趣参数的平均估计问题,并且对删失响应变量的不同水平分位数进行建模,以全面反映响应变量分布特征,有效克服异常值和厚尾模型误差的影响.基于扩展的兴趣信息准则给出参数的平均估计方法,证明估计的渐近性质.通过Monte Carlo随机模拟试验比较所提估计方法和最小二乘方法在有限样本量下的表现,用所提方法对原发性胆汁性肝硬化数据集进行数据分析.     

Variable selection and coefficient estimation via composite quantile regression with randomly censored data

Composite quantile regression with randomly censored data is studied. Moreover, adaptive LASSO methods for composite quantile regression with randomly censored data are proposed. The consistency, asymptotic normality and oracle property of the proposed estimators are established. The proposals are illustrated via simulation studies and the Australian AIDS dataset.