不完全数据推断方法的进一步讨论

项目名称： 不完全数据推断方法的进一步讨论

项目编号： No.11271286

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 梁汉营

作者单位： 同济大学

项目金额： 60万元

中文摘要： 应用核估计、局部多项式估计、非线性小波估计和经验似然等技术以及综合应用其中的方法，研究在相依假设下，左截断与右删失样本或在发生数据随机丢失条件下的非参数估计、以及预光滑估计的统计推断问题，具体的研究包括非参数回归函数核估计与局部M估计、密度函数估计、条件密度函数估计、分位数估计、条件分位数估计、以及条件mode估计的渐近性质和假设检验等问题。基于Copula函数构造并研究不完全样本条件密度函数估计的渐近性质。对回归模型，在反应变量发生删失或数据丢失的情况下，研究回归函数及未知参数估计的大样本性质，包括未知参数的Jackknife推断。同时研究不完全数据的经验似然与Jackknife经验似然，以及左截断或右删失样本的Jackknife推断。利用实际数据对理论结果进行模拟验证，并探索理论结果在实际问题中的应用。

中文关键词： 不完全数据；非参数估计；经验似然；回归模型；非线性小波

英文摘要： By applying the estimate methods of kernel,local polynomial, wavelet, empirical likelihood as well as their synthesis, we investigate the statistical inference questions related to nonparametric estimation and presmoothed estimation for left truncated and right censored data,and/or missing data with dependent observations. In particular, the study includes asymptotic properties of estimators and hypothesis test for regression function, density function, conditional density function, quantile, conditional quantile and conditional mode. The properties of the estimators of conditional density for the incomplete samples based on Copula function are studied. Large sample properties of estimators for regression function and unknown parameter,including Jackknife inference for unknown parameter, in regression model with responses missing at random or censoring are deduced. Meanwhile,the empirical likelihood and Jackknife empirical likelihood for incomplete data, as well as Jackknife inference for left truncated or right censored samples are discussed. Simulation study is done to investigate the finite sample performance of the proposed estimators. Applications in practice questions of the obtained theoretical results are explored.

英文关键词： Incomplete data；Nonparametric estimation；Empirical likelihood；Regression model；Nonlinear wavelet