Smoothing and nonparametric tests

平滑和非参数检验

• 批准号: 250062-2006
• 负责人: Zhang, Jin
• 金额: $ 0.8万
• 依托单位: University of Manitoba
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2006
• 资助国家: 加拿大
• 起止时间: 2006-01-01 至 2007-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=334365
• 关键词: Smoothing; nonparametric; tests

A fundamental problem in data analysis is to check how well a statistical model fits observed data. Nonparametric smoothing and testing methods provide convenient and powerful tools for model building and checking, as well as goodness-of-fit tests for parametric models. Smoothing is a major subject in modern nonparametric statistics. Density estimation is a basic issue in nonparametric smoothing, testing, and many important statistical problems. A good method of density estimation is essential for developing new methodologies of smoothing and powerful nonparametric tests based on the likelihood ratio. Density estimation has been a hot topic in the statistical literature. The most popular method is kernel density estimation, for which the critical problem is bandwidth selection for balancing smoothness and accuracy. Bandwidth selection is also crucial to general kernel smoothing methods for nonparametric models. A large or small bandwidth will over or under smooth the kernel model. Quick-simple methods are easy to apply but perform poor for complicated models. On the other hand, the existing hi-tech methods have computational difficulty, and do not have solutions occasionally. A data-driven bandwidth is highly demanded, which is easy to apply and suits for various kinds of models. One possible solution is to use an initial fixed (global) bandwidth to build a variable (local) bandwidth, or to use other localized smoothing techniques. The results of this research are useful in developing new technologies for nonparametric modeling and testing.

数据分析中的一个基本问题是检查统计模型与观测数据的拟合程度。非参数平滑和检验方法为模型的建立和检验以及参数模型的拟合优度检验提供了方便而强大的工具。平滑是现代非参数统计学的一个重要课题。密度估计是非参数平滑、检验和许多重要统计问题中的一个基本问题。一个好的密度估计方法是必不可少的，以发展新的平滑和强大的非参数检验方法的基础上的似然比。密度估计一直是统计文献中的一个热门话题。最流行的方法是核密度估计，其关键问题是平衡平滑性和准确性的带宽选择。对于非参数模型的一般核平滑方法，带宽选择也是至关重要的。大或小的带宽将使内核模型过度平滑或欠平滑。快速简单的方法很容易应用，但对复杂的模型表现不佳。另一方面，现有的高技术方法计算困难，有时没有解决方案。数据驱动的带宽要求很高，易于应用，适用于各种型号。一种可能的解决方案是使用初始固定（全局）带宽来构建可变（局部）带宽，或者使用其他局部平滑技术。本研究的结果对于开发非参数建模和测试的新技术是有用的。