Smoothing and nonparametric tests

点击翻译按钮获取中文摘要

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.