高维非参数模型(可加模型，多指标可加模型)的直接变量选择和估计

项目名称： 高维非参数模型(可加模型，多指标可加模型)的直接变量选择和估计

项目编号： No.11301434

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 冯峥晖

作者单位： 厦门大学

项目金额： 23万元

中文摘要： 在众多统计建模方法中，非参数方法以其对模型已知信息要求少，灵活性高而备受关注，在生物医学、经济、环境等领域中有着广泛的应用前景。本项目将重点研究维数较高的非参数模型，主要包括非参数可加模型和多指标可加模型的变量选择、估计及应用问题。在理论方面，不同于现有的非参数模型的变量选择方法，我们提出非参数模型直接变量选择的方法，而不需要对模型进行近似，并将证明它的大样本性质。进一步，用此方法对可加模型和多指标可加模型进行变量选择，根据模型的特性分别提出新的两步估计方法和改进的交替最优算法，证明它们的理论性质。上述方法不仅对高维非参数模型成立，对于普通的非参数模型也适用。在应用方面，将用上述方法分析多因素环境数据，挑选对因变量起重要作用的环境指标，并估计它们之间的函数关系，为实际分析提供新的工具。

中文关键词： 非参数模型；变量选择；非参数可加模型；渐近性质；可适应性估计

英文摘要： Because of the flexibility and the less need of information, the nonparametric models attract a lot of interest among most of model building methods. There are large potential applications for this model in biomedicine, economics, environmental science and other fields. This proposal focuses on studying the variable selction and estimation for high dimensional nonparametric models, including the nonparametric additive models and the nonparametric multi-index additive models. In theory, we propose a direct model selection method for nonparametric models. This method could select out the important variables directly without any nonparametric approximation. Large sample theories will be proven. Furthermore, model selection for the nonparametric additive models and the multi-index additive models are conducted based on our direct method, and thus we propose new two-step estimation methods and adjusted ADO methods. Large sample properties will be discussed. Our methods work not only in high dimensional nonparametric models, but also in ordinary dimensional models. In the application, our methods are propsoed to analyze multi-variable environmental data, selecting out the improtant indices(variables), and estimating the functions between these indices and the dependent variable. This will provide a new tool for enviro

英文关键词： Nomparametric Models；Variable Selection；Nonparametric Addtive Models；Asymptotic Property；Adaptive Estimation