Mathematical Sciences: Smoothing Parameters and Model Selection

首席研究员将研究 非参数的平滑参数（带宽）选择 模型和线性模型的阶数选择。 非参数 线性模型在许多领域得到了广泛的应用。 尽管有许多过程可用于选择 带宽或顺序，这是公认的，经典的 选择器受到大的样本变化的影响，因此可以 在实践中没有多大用处。 最近，利用这项技术， 傅立叶分析，研究人员提出了一些稳定的 减少选择带宽变化的程序 密度估计的核回归 该项目将 遵循研究人员最近获得的方法， 研究带宽或阶数选择问题， 重要的情况，其中包括边界效应，随机设计 点，自回归过程的阶数选择，提取 周期分量、点过程和鲁棒平滑器。

The principal investigator will study the problems of smoothing parameter (bandwidth) selection for nonparametric models, and order selection for linear models. Nonparametric and linear models have been used extensively in many fields. Although there are many procedures available for selecting the bandwidth or the order, it is recognized that the classical selectors are subject to large sample variation, and thus may not be very useful in practice. Recently, using the technique of Fourier analysis, the investigator proposed some stabilized procedures to reduce the variation in selecting the bandwidth for kernel regression of density estimation. This project will follow the approach recently obtained by the investigator to study the bandwidth or order selection problems for several important cases, which include boundary effects, random design points, order selection for autoregressive processes, extraction of periodic components, point processes, and robust smoothers.