From finite sample to asymptotics: A geometric bridge for selection criteria in spline regression

Semiparametric Penalized Spline Regression

In this paper, we propose a new semiparametric regression estimator by using a hybrid technique of a parametric approach and a nonparametric penalized spline method. The overall shape of the true regression function is captured by the parametric part, while its residual is consistently estimated by the nonparametric part. Asymptotic theory for the proposed semiparametric estimator is developed, showing that its behavior is dependent on the asymptotics for the nonparametric penalized spline estimator as well as on the discrepancy between the true regression function and the parametric part. As …

Functional Group Bridge for Simultaneous Regression and Support Estimation

This article is motivated by studying multisensory effects on brain activities in intracranial electroencephalography (iEEG) experiments. Differential brain activities to multisensory stimulus presentations are zero in most regions and non-zero in some local regions, yielding locally sparse functions. Such studies are essentially a function-on-scalar regression problem, with interest being focused not only on estimating nonparametric functions but also on recovering the function supports. We propose a weighted group bridge approach for simultaneous function estimation and support recovery in f…

具有流形约束和复合二次惩罚的多任务函数线性回归模型的统一分析

A Unified Analysis of Multi-task Functional Linear Regression Models with Manifold Constraint and Composite Quadratic Penalty

本文研究多任务函数线性回归模型，提出具有矩阵流形约束和复合二次惩罚的双重正则化通用模型，推导出统一的收敛上界并应用于降秩和图拉普拉斯正则化等特例。

用于椭圆马氏判别分析的闭式分数径向链接

Closed-form fractional radial links for elliptical Mahalanobis discriminant analysis

研究共享生成器椭圆类条件分布下二元分类，通过有限分数幂随机多项式投影推导贝叶斯径向链接族，在多个数据集验证效果，相比全局GAM无显著损失，比QDA在重尾序列表现更好，提高了分类准确性。