含指标项的变换模型的估计与经验似然分析

项目名称： 含指标项的变换模型的估计与经验似然分析

项目编号： No.11201190

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 李建波

作者单位： 江苏师范大学

项目金额： 22万元

中文摘要： 线性变换模型是一类响应变量为寿命时间未知单调递增变换的线性回归模型，该变换保持寿命时间的秩，从而该模型在寿命数据建模方面具有非常好的灵活性和简洁性。基于删失寿命数据，本项目拟推广线性变换模型，研究含有指标项的半参数变换模型的估计与经验似然分析问题。该类模型集线性变换模型和非参数变换模型优点于一身，既能避免"维数祸根"问题又能体现高维数据特征。利用样条多项式、局部多项式等逼近技术和估计方程、极大似然等估计方法，研究这类变换模型中未知参数和未知函数的估计问题及其大样本性质；通过经验似然方法，研究模型中未知参数的置信域和未知函数的置信带构造问题，同时给出经验似然比统计量的大样本性质；最后我们把该类模型的理论研究成果应用到临床医学，经济学，金融学，生物学等领域。通过系统研究此类模型不仅能够丰富变换模型的理论内容，而且能够拓广单指标技术研究方法的应用领域。

中文关键词： 单指标半参数模型；B样条逼近；局部多项式逼近；估计；经验似然

英文摘要： Linear transformation models are a class of linear regression models with an unknown increasing transformation for respose variable, in which the transformation preserves rankings for life times. Therefore the class of models can enjoy good conciseness and flexibility in survival data modeling. Based on censored survival data, we will generalize linear transformation models and study the semiparametric transformation models with index term. In this project, we mainly consider estimation and empirical likelihood inference for this class of models. This class of models have advantages of both linear transformation models and nonparametric transformation models. They not only can avoid "Curse of Dimensionality" but also can capture important features in high-dimensional data. By use of spline polynomial or locally polynomial approximation techniques and estimation function or maximum likelihood estimation methods, we study the estimation of unknown parameters and functions in these models. Moreover, we also give large sample properties and convergence ratio for all the estimates. By virtue of empirical likelihood approach, we will establish confidence interval for unknown parameters and confidence band for unknown functions in these models. At the same time, we will investigate the large sample properties of empir

英文关键词： Single index semiparametric model；B spline approximation；Local polynomial approximation；Estimation；Empirical likelihood