对称及偏斜对称分布族下测量误差模型的稳健估计与诊断研究

项目名称： 对称及偏斜对称分布族下测量误差模型的稳健估计与诊断研究

项目编号： No.11301278

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： 曹春正

作者单位： 南京信息工程大学

项目金额： 23万元

中文摘要： 测量误差广泛存在于各类实际数据中，是当今统计学研究热点之一。对于该类数据，若依指定分布建模则很可能产生分布误判下的推断偏差，基于对称和偏斜对称分布族建模能够有效地避免或缓解这一问题。本项目拟研究对称和偏斜对称分布族下测量误差模型的统计推断及诊断问题，旨在建立分布族下测量误差模型的一致估计式和诊断度量，以期获得更为稳健、可靠的统计分析结果。本项目首先基于对称分布对复杂测量误差数据进行模型构建，并利用正态尺度混合分布的多层结构建立EM估计、回归校正和模拟外推等估计方法，导出估计量的渐近性质；其次，研究模型的异方差检验、兴趣参数检验和分布对称性检验方法，给出检验统计量的渐近性质和检验功效，并基于Q距离和K-L距离建立影响分析度量；此外，将对称分布测量误差模型的统计推断和诊断理论发展至偏斜对称分布模型，构建相应的估计理论和诊断度量。本项研究将有助于研究者更为科学地分析含有测量误差的复杂数据。

中文关键词： 对称分布；偏斜对称分布；测量误差模型；稳健估计；统计诊断

英文摘要： Measurement error (ME) is widely found in various types of real data, and is one of the hot research topic in statistics today. In the analysis of such data, it is likely to induce inference bias due to the misspecification of the distribution. However, this problem can be avoided or alleviated when the symmetrical and skew-symmetrical distribution classes are used to modeling. This project will study statistical inferences and diagnostics of the ME model under symmetrical and skew-symmetrical distributions. We aim to establish consistent forms of the estimations and diagnostic metrics for the ME model under the distribution classes, in order to obtain more robust, reliable statistical analysis results. Firstly, we propose to model the complicated ME data by the symmetrical distributions. Based on the hierarchical structure of scale mixtures of normal distributions, the EM, regression calibration, simulation and extrapolation estimation methods will be constructed. The asymptotic properties of the estimators will also be given. Secondly, hypothesis tests, such as heteroscedasticity, interest parameters and the symmetry of the distribution will be studied, together with the asymptotic properties and powers of the test statistics. Based on the Q distance and K-L divergence, the influence analysis will also be deri

英文关键词： Symmetrical distribution；Skew-symmetrical distribution；Measurement error model；Robust estimation；Statistical diagnostic